# Homework Help: ODE - Comining Undetermined Coefficients Method with Variation of Parameters Method

1. May 16, 2010

### gabriels-horn

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up?

1. The problem statement, all variables and given/known data

3. The attempt at a solution
I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My guess would be to use the VOP method for the (1/x)*e^x portion and the undetermined coefficients for the 4x^2-3 portion. Any pointers?

Last edited: May 17, 2010
2. May 16, 2010

### LCKurtz

Re: ODE - Comining Undetermined Coefficients Method with Variation of Parameters Meth

You have the right idea. I will call the left side of your equation L(y) for brevity.

Your complementary solution yc satisfies the homogeneous equation

L(y) = 0. Now if you have two particular solutions satisfying L(yp1) = f(x) and L(yp2) = g(x), then

L(yp1+yp2) = L(yp1)+L(yp1) = f(x)+g(x)

so find the two particular solutions separately as you have indicated, and add them to your yc.

3. May 16, 2010

### gabriels-horn

Re: ODE - Comining Undetermined Coefficients Method with Variation of Parameters Meth

Great, thanks for the insight.