• #### what is solution of y'-y^2-x-x^2=0 it seems wolfram solution is wrong?

From drhuang57@gmail.com@21:1/5 to All on Tue Feb 2 16:50:46 2021
what is solution of y'-y^2-x-x^2=0
it seems wolfram solution is wrong?

mathHand.com

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• From Nasser M. Abbasi@21:1/5 to drhu...@gmail.com on Wed Feb 3 01:19:28 2021
On 2/2/2021 6:50 PM, drhu...@gmail.com wrote:
what is solution of y'-y^2-x-x^2=0
it seems wolfram solution is wrong?

mathHand.com

I added this ODE. You can find its solution here

https://www.12000.org/my_notes/solving_ODE/current_version/insu3828.htm#x4044-458900032.1.93

This is also a Riccati ODE. It solved by transforming it to a
second order ODE in u(x) with variable conditions. This second
order ODE is then solved, and its solution u(x) is then
transfored back to y(x).

===================================
ode:=diff(y(x),x)-y(x)^2-x-x^2=0;

mysol:= y(x) = ((48*I*x^2 + 48*I*x - 48 + 12*I)*hypergeom([3/4 - I/16], [3/2], I/4*(2*x + 1)^2) - 48*(((1/12 + I)*x + 1/24 + I/2)
*hypergeom([7/4 - I/16], [5/2], I/4*(2*x + 1)^2) - _C0*(-(1/4 + I) *hypergeom([5/4 - I/16], [3/2], I/4*(2*x + 1)^2)
+ hypergeom([1/4 - I/16], [1/2], I/4*(2*x + 1)^2)*I)/2)
*(x + 1/2))/((48*x + 24)*hypergeom([3/4 - I/16], [3/2], I/4*(2*x + 1)^2)
+ 24*_C0*hypergeom([1/4 - I/16], [1/2], I/4*(2*x + 1)^2))

odetest(mysol,ode)
0
================================

The solution given by Wolfram alpha as y(x) = 1/(c-x) is clearly
wrong as it does not satisfy the ode. You might want to send bug report
of DSolve as Mathematica 12.2.

Both Maple 2020.2 and Mathematica 12.2 also solve this.

--Nasser

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• From Jens Kallup@21:1/5 to All on Fri May 14 11:18:44 2021
Am 03.02.2021 um 01:50 schrieb drhu...@gmail.com:
what is solution of y'-y^2-x-x^2=0
it seems wolfram solution is wrong?

mathHand.com

Hello,

as hobbit, i would say:

y^1 - y^2 - x^1 - x^2 = 0 | -y^1 ( y^2 - y^1)
- y^1 - x^1 + x^1 = -y | +x^1 (-x^1 + x^1 | -x^2 + x^1)

A A
+-----------------+
A | A A A
+-----o-----------------+-----------+------------+
| |
V V

- y^1 0 + x = -y -x
-------------------------------
- y^1 -x^0 + x^1 = 0
- 1 0 + 1 = 0 | voila: result is 0. ===============================

best viewed with fixed font weight (Courier/Courier New).
So, where should be a bug/wrong/mistake ?

Jens

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