Please show me a solution to the differential equation

[edgepflow]

Can someone solve:

y''(x) - A x^2 y = 0

A = constant

It is probably easy, but I took this class 23 years ago.

 

[LightningStrike]

This one's not so easy as far as I can tell. Fortunately others have figured it out already: http://eqworld.ipmnet.ru/en/solutions/ode/ode0202.pdf

Here's a great website when you have an ODE that you think someone might have solved before: http://eqworld.ipmnet.ru/en/solutions/ode.htm

I referred to the book the authors of that website have written. They have some different things written about a more general form of this equation. This book might be worth tracking down if the link above doesn't help.

 

[edgepflow]

Thanks btrettel! I had a feeling that equation had an attitude.

Now I will grind out some Bessel functions.

 

[masqau]

Its solution is not Bessel Function. Its a Harmonic Oscillator.
its solution must be some constant with exp(x^2).
the differential equation for Bessel function is
x^2Y''+xY'+(x^2-n^2)y=0
which is of course not ur differential equation.