• #### what is solution of y'-y^2-x^2-1=0 ? it seems wolfram solution is wrong

From drhuang57@gmail.com@21:1/5 to All on Thu Feb 4 15:56:07 2021
what is solution of y'-y^2-x^2-1=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 Thu Feb 4 18:25:12 2021
On 2/4/2021 5:56 PM, drhu...@gmail.com wrote:
what is solution of y'-y^2-x^2-1=0 ?
it seems wolfram solution is wrong?

mathHand.com

I happend to have solved this ode allready, but with +1
instead of -1. It is ofcourse a RICCATI ODE. The solution
follows the same algorithm.

You can find the solution here

https://www.12000.org/my_notes/solving_ODE/current_version/insu3821.htm

For -1, instead of +1, the solution is

===========
ode:=ode:=diff(y(x),x) -x^2-y(x)^2-1=0;
y(x) = 1/2*((-3+I)*_C0*WhittakerM(1-1/4*I,1/4,I*x^2)+4*WhittakerW(1-1/4*I,1/4,I *x^2)+(-2*I*x^2+1-I)*_C0*WhittakerM(-1/4*I,1/4,I*x^2)+(-2*I*x^2+1-I)*WhittakerW (-1/4*I,1/4,I*x^2))/x/(WhittakerW(-1/4*I,1/4,I*x^2)+_C0*WhittakerM(-1/4*I,1/4,I *x^2));
odetest(mysol,ode);
0
=================

Wolfram alpha solution is again wrong. It looks like Wolfram alpha
has a bug with Riccati ODE's. You might want to consider reporting
these to them so they can fix it.

--Nasser

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