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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