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  • how to check solution?

    From Dr Huang@21:1/5 to All on Thu Jun 23 22:32:43 2022
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com

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  • From Axel Vogt@21:1/5 to All on Sun Jun 26 21:19:19 2022
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com

    Why should it be 'simple'? I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'.

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  • From Dr Huang@21:1/5 to Axel Vogt on Sun Jun 26 17:23:20 2022
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'.

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Axel Vogt@21:1/5 to All on Mon Jun 27 06:40:57 2022
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert
    Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'.

    And what is your solution?

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  • From Dr Huang@21:1/5 to Axel Vogt on Mon Jun 27 20:16:59 2022
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert
    Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'. And what is your solution?

    Input your ODE into mathHand.com, click the ODE button to solve, or click http://server.drhuang.com/input/i=y(2,x)=y^2-y
    then click the test button to test solution

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Dr Huang@21:1/5 to Axel Vogt on Mon Jun 27 20:20:26 2022
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert
    Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'. And what is your solution?

    Input your ODE into mathHand.com, click the ODE button to solve, or click http://server.drhuang.com/input/?guess=dsolve%28y%282%2Cx%29%3Dy%5E2-y%29&inp=y%282%2Cx%29%3Dy%5E2-y
    then click the test button to test solution

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  • From Dr Huang@21:1/5 to Dr Huang on Mon Jun 27 20:30:46 2022
    On Tuesday, 28 June 2022 at 13:20:29 UTC+10, Dr Huang wrote:
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert >> Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of
    the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it
    is in EllipticF of the (complicated) roots of the cubic. Besides then
    solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'. And what is your solution?
    Input your ODE into mathHand.com, click the ODE button to solve, or click http://server.drhuang.com/input/?guess=dsolve%28y%282%2Cx%29%3Dy%5E2-y%29&inp=y%282%2Cx%29%3Dy%5E2-y
    then click the test button to test solution

    http://server.drhuang.com/input/?guess=dsolve(y(2,x)=y**2-y)

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  • From Axel Vogt@21:1/5 to All on Tue Jun 28 12:05:52 2022
    Am 28.06.2022 um 05:30 schrieb Dr Huang:
    On Tuesday, 28 June 2022 at 13:20:29 UTC+10, Dr Huang wrote:
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert >>>>> Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of >>>>> the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it >>>>> is in EllipticF of the (complicated) roots of the cubic. Besides then >>>>> solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'. >>> And what is your solution?
    Input your ODE into mathHand.com, click the ODE button to solve, or click
    http://server.drhuang.com/input/?guess=dsolve%28y%282%2Cx%29%3Dy%5E2-y%29&inp=y%282%2Cx%29%3Dy%5E2-y
    then click the test button to test solution


    http://server.drhuang.com/input/?guess=dsolve(y(2,x)=y**2-y)

    That link works. So you say it is 1/2+weierstrassP(C_1+x,1/2,C_2)
    and no restriction for the constants (?).

    What is your convention for weierstrassP ?

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  • From antispam@math.uni.wroc.pl@21:1/5 to Axel Vogt on Tue Jun 28 11:16:58 2022
    Axel Vogt <//noreply@axelvogt.de> wrote:
    Am 28.06.2022 um 05:30 schrieb Dr Huang:
    On Tuesday, 28 June 2022 at 13:20:29 UTC+10, Dr Huang wrote:
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert >>>>> Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of >>>>> the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it >>>>> is in EllipticF of the (complicated) roots of the cubic. Besides then >>>>> solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'.
    And what is your solution?
    Input your ODE into mathHand.com, click the ODE button to solve, or click >> http://server.drhuang.com/input/?guess=dsolve%28y%282%2Cx%29%3Dy%5E2-y%29&inp=y%282%2Cx%29%3Dy%5E2-y
    then click the test button to test solution


    http://server.drhuang.com/input/?guess=dsolve(y(2,x)=y**2-y)

    That link works. So you say it is 1/2+weierstrassP(C_1+x,1/2,C_2)
    and no restriction for the constants (?).

    What is your convention for weierstrassP ?

    In FriCAS:

    (22) -> f := 1/2 + 6*weierstrassP(1/12, g2, c1 + x)

    1
    12 weierstrassP(--,g2,x + c1) + 1
    12
    (22) ---------------------------------
    2
    Type: Expression(Integer) (23) -> D(f, x, 2) - (f^2 - f)

    (23) 0
    Type: Expression(Integer)

    There is also trival solution, that is f := 1. FriCAS definition
    of weierstrassP is rather conventional:

    (25) -> D(weierstrassP(g2, g3, x), x)

    (25) weierstrassPPrime(g2,g3,x)
    Type: Expression(Integer) (26) -> D(weierstrassPPrime(g2,g3,x), x)

    2
    12 weierstrassP(g2,g3,x) - g2
    (26) ------------------------------
    2
    Type: Expression(Integer)

    There seem to be some confusion about order of arguments and
    apparently Dr Huang skipped factor of 6 from derivative
    of weierstrassPPrime (or whatever he uses instead).

    --
    Waldek Hebisch

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  • From Axel Vogt@21:1/5 to All on Tue Jun 28 18:39:15 2022
    Am 28.06.2022 um 13:16 schrieb antispam@math.uni.wroc.pl:
    Axel Vogt <//noreply@axelvogt.de> wrote:
    Am 28.06.2022 um 05:30 schrieb Dr Huang:
    On Tuesday, 28 June 2022 at 13:20:29 UTC+10, Dr Huang wrote:
    On Monday, 27 June 2022 at 14:41:01 UTC+10, Axel Vogt wrote:
    Am 27.06.2022 um 02:23 schrieb Dr Huang:
    On Monday, 27 June 2022 at 05:19:22 UTC+10, Axel Vogt wrote:
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com
    Why should it be 'simple'?
    Because a simple solution is easy to undersand, plot and check. Why cannot maple find a simple solution? e.g. there are over such 700 ODE in http://drhuang.com/index/bug

    I am not into ODE and using Maple it gives
    an implicit solution which essentially tells me that one has to invert >>>>>>> Int(1/((6*a^3-9*a^2+9*c)^(1/2)), a = 0 .. z) for z, c is a quadric of >>>>>>> the values for f(0) and f'(0).

    In rare cases for c that elliptic integral is 'simple', in general it >>>>>>> is in EllipticF of the (complicated) roots of the cubic. Besides then >>>>>>> solving for z.

    The implict solution can be 'comfirmed' using Maple's command 'odetest'.
    And what is your solution?
    Input your ODE into mathHand.com, click the ODE button to solve, or click >>>> http://server.drhuang.com/input/?guess=dsolve%28y%282%2Cx%29%3Dy%5E2-y%29&inp=y%282%2Cx%29%3Dy%5E2-y
    then click the test button to test solution


    http://server.drhuang.com/input/?guess=dsolve(y(2,x)=y**2-y)

    That link works. So you say it is 1/2+weierstrassP(C_1+x,1/2,C_2)
    and no restriction for the constants (?).

    What is your convention for weierstrassP ?

    In FriCAS:

    (22) -> f := 1/2 + 6*weierstrassP(1/12, g2, c1 + x)

    1
    12 weierstrassP(--,g2,x + c1) + 1
    12
    (22) ---------------------------------
    2
    Type: Expression(Integer)
    (23) -> D(f, x, 2) - (f^2 - f)

    (23) 0
    Type: Expression(Integer)

    There is also trival solution, that is f := 1. FriCAS definition
    of weierstrassP is rather conventional:

    (25) -> D(weierstrassP(g2, g3, x), x)

    (25) weierstrassPPrime(g2,g3,x)
    Type: Expression(Integer)
    (26) -> D(weierstrassPPrime(g2,g3,x), x)

    2
    12 weierstrassP(g2,g3,x) - g2
    (26) ------------------------------
    2
    Type: Expression(Integer)

    There seem to be some confusion about order of arguments and
    apparently Dr Huang skipped factor of 6 from derivative
    of weierstrassPPrime (or whatever he uses instead).



    Maple (and Mathematica?) uses the following:

    diff(f(z), z$2) = 6*f(z)^2-1/2*g2
    has solution
    f(z) = WeierstrassP(z+_C1,g2,_C2)

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  • From Axel Vogt@21:1/5 to All on Wed Jun 29 19:54:37 2022
    Am 28.06.2022 um 13:16 schrieb antispam@math.uni.wroc.pl:
    In FriCAS:

    (22) -> f := 1/2 + 6*weierstrassP(1/12, g2, c1 + x)

    1
    12 weierstrassP(--,g2,x + c1) + 1
    12
    (22) ---------------------------------
    2
    Type: Expression(Integer)
    (23) -> D(f, x, 2) - (f^2 - f)

    (23) 0
    Type: Expression(Integer)

    There is also trival solution, that is f := 1. FriCAS definition
    of weierstrassP is rather conventional

    Thank you.
    In Maple I used: f(x) =1/2 + 6*WeierstrassP(c1 + x, 1/12, c2);
    odetest(%, ode) confirming it

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  • From Axel Vogt@21:1/5 to All on Thu Jun 30 20:08:08 2022
    Am 24.06.2022 um 07:32 schrieb Dr Huang:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com

    Somewhat related:

    for f'' = f^2 you site gives a rational function 6*(C_1 +- x)^(-2), http://server.drhuang.com/input/?guess=dsolve(y(2,x)=y**2),
    only one parameter

    However Maple gives 6*WeierstrassP(z+_C1,0,_C2) for which your output
    is a special and limiting case (discriminant = 0)

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  • From Kristjan Robam@21:1/5 to All on Tue Jul 12 23:26:05 2022
    (_!_)

    drhu...@gmail.com kirjutas Reede, 24. juuni 2022 kl 07:32:45 UTC+2:
    wolfram give very complicated solution for
    y''=y^2-y
    how to check its solution?

    DrHuang.com

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)