# Thread: Solve using method of variation of parameters

1. ## Solve using method of variation of parameters

Maybe you can help me with this ODE question? It says to use the method of variation of parameters to find the general solution to

y'' + xy' + y = xe^(-x^2/2) given that one solution is e^(-x^2/2) and the other is that sum of series.

The only way I know how to do this is by solving for two functions v1' and v2' but the series is throwing me off.

If you have any ideas that would be great.

2. Originally Posted by sarah232
Maybe you can help me with this ODE question? It says to use the method of variation of parameters to find the general solution to

y'' + xy' + y = xe^(-x^2/2) given that one solution is e^(-x^2/2) and the other is that sum of series.

The only way I know how to do this is by solving for two functions v1' and v2' but the series is throwing me off.

If you have any ideas that would be great.
Using a variation of parameters could get a little cumbersome, especially with one solution a series solution. Another way is to use a reduction of order type idea. Let

$y = u \,e^{-x^2/2}$

which substituting into your ODE gives

$
u'' - xu' -x = 0.
$