what is solution of y'-y^2-x-x^2=0 it seems wolfram solution is wrong? mathHand.com

[drhu...@gmail.com]

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

mathHand.com

[Nasser M. Abbasi]

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
to Wolfram Alpha about this. May be they are not using same version
of DSolve as Mathematica 12.2.

Both Maple 2020.2 and Mathematica 12.2 also solve this.

--Nasser

[Jens Kallup]

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