# Find one solution of the differential eqn

• Apr 28th 2009, 10:44 AM
sarah232
Find one solution of the differential eqn
Here is the question:

Use a change of independent variable to find ONE solution of

y''(t) + e^(2t)y(t) = 0

in terms of the Bessel Function of order 0.

I'm not sure where to start or where the Bessel function comes in.
• Apr 28th 2009, 04:58 PM
Jester
Quote:

Originally Posted by sarah232
Here is the question:

Use a change of independent variable to find ONE solution of

y''(t) + e^(2t)y(t) = 0

in terms of the Bessel Function of order 0.

I'm not sure where to start or where the Bessel function comes in.

With your equation, I might divide by $e^{2t}$ which gives

$\frac{1}{e^{2t}} y'' + y = 0$ or $e^{-2t} y'' + y = 0$ then try letting $x = e^{t}$ .