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  • what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y

    From Dr Huang (DrHuang.com)@21:1/5 to All on Wed Oct 4 05:46:18 2023
    wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?

    mathhand.com gives a simple solution and auto plot the solution

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  • From Nasser M. Abbasi@21:1/5 to All on Thu Oct 5 02:35:24 2023
    On 10/4/2023 7:46 AM, Dr Huang (DrHuang.com) wrote:
    wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?

    mathhand.com gives a simple solution and auto plot the solution



    What is the solution you obtained?

    I solved it and got

    exp(x)*sin(y(x)) + x*tan(y(x)) = c_1

    Where c_1 is constant of integration. Here is my solution

    https://12000.org/tmp/10052023/main.pdf

    This is an easy ode to solve as it is exact ode.

    Mathematica 13.3.1 gives complicated answer because its answer is explicit.

    Mathematica DSolve does not have an option to ask for an implicit solution
    like with Maple's dsolve.

    ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
    DSolve[ode, y[x], x]

    The answer is long, because it tried to solve for y from the solution above. That is all. It will be nice if DSolve has an option asking for implicit solution to an ode.

    --Nasser

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  • From Dr Huang (DrHuang.com)@21:1/5 to Nasser M. Abbasi on Thu Oct 5 17:17:24 2023
    On Thursday, 5 October 2023 at 18:35:28 UTC+11, Nasser M. Abbasi wrote:
    On 10/4/2023 7:46 AM, Dr Huang (DrHuang.com) wrote:
    wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?

    mathhand.com gives a simple solution and auto plot the solution


    What is the solution you obtained?

    I solved it and got

    exp(x)*sin(y(x)) + x*tan(y(x)) = c_1

    Where c_1 is constant of integration. Here is my solution

    https://12000.org/tmp/10052023/main.pdf
    thanks


    This is an easy ode to solve as it is exact ode.
    you are right, this is an easy ode to solve. but wolfram make a simple solution to complicated.


    Mathematica 13.3.1 gives complicated answer because its answer is explicit.

    Mathematica DSolve does not have an option to ask for an implicit solution like with Maple's dsolve.

    ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
    DSolve[ode, y[x], x]

    The answer is long, because it tried to solve for y from the solution above. That is all. It will be nice if DSolve has an option asking for implicit solution to an ode.
    how to check its solution?


    --Nasser
    Thanks

    --------------
    mathHand.com

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  • From Nasser M. Abbasi@21:1/5 to All on Thu Oct 5 21:59:02 2023
    On 10/5/2023 7:17 PM, Dr Huang (DrHuang.com) wrote:

    The answer is long, because it tried to solve for y from the solution above. >> That is all. It will be nice if DSolve has an option asking for implicit
    solution to an ode.

    how to check its solution?


    The method to check solution for ode in Mathematica is given in

    https://reference.wolfram.com/language/howto/CheckTheResultsOfDSolve.html

    Basically, you do

    ode=y'[x]+y[x]==0;
    sol=DSolve[ode,y,x];
    ode/.sol//Simplify

    {True}

    Since it returned True, then the solution is correct, as it means it
    satisfies the ode.

    For your example, it is the same thing

    ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
    sol = DSolve[ode, y, x];
    ode /. sol // Simplify

    But since the solution is very complicated, it was taking too long to finish for me to wait so I stopped it after 10 minutes.

    Note to use the above, you need to use the format DSolve[ode, y, x] and
    not DSolve[ode, y[x], x];

    --Nasser

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  • From Dr Huang (DrHuang.com)@21:1/5 to Nasser M. Abbasi on Thu Oct 5 20:25:06 2023
    On Friday, 6 October 2023 at 13:59:08 UTC+11, Nasser M. Abbasi wrote:
    On 10/5/2023 7:17 PM, Dr Huang (DrHuang.com) wrote:

    The answer is long, because it tried to solve for y from the solution above.
    That is all. It will be nice if DSolve has an option asking for implicit >> solution to an ode.

    how to check its solution?

    The method to check solution for ode in Mathematica is given in

    https://reference.wolfram.com/language/howto/CheckTheResultsOfDSolve.html

    Basically, you do

    ode=y'[x]+y[x]==0;
    sol=DSolve[ode,y,x];
    ode/.sol//Simplify

    {True}

    Since it returned True, then the solution is correct, as it means it satisfies the ode.

    For your example, it is the same thing
    ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
    sol = DSolve[ode, y, x];
    ode /. sol // Simplify

    But since the solution is very complicated, it was taking too long to finish for me to wait so I stopped it after 10 minutes.

    Note to use the above, you need to use the format DSolve[ode, y, x] and
    not DSolve[ode, y[x], x];

    --Nasser
    How to check its solution with wolfram alpha?
    Can it be easy to check by a click? as check solution by a click the test button in mathhand.com?

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