Reviewing for finals. Fun! I'd like to better understand the approach to this kind of problem:

I have a second order linear differential equation, y''-9y=0, with two solutions, y1=e^3x, y2=e^(-3x), with y(0)=-1 and y'(0)=15.

First, I want to verify that y1 and y2 are solutions.
Second, I want to find a particular solution using given the initial conditions. I'll post as I work on it, but any help would be great. Thanks! :)

Question

Reviewing for finals. Fun! I'd like to better understand the approach to this kind of problem: 

I have a second order linear differential equation, y''-9y=0, with two solutions, y1=e^3x, y2=e^(-3x), with y(0)=-1 and y'(0)=15. 

First, I want to verify that y1 and y2 are solutions. 
Second, I want to find a particular solution using given the initial conditions. I'll post as I work on it, but any help would be great. Thanks! :)

anonymous · Answer

Ok, I think I have it! See the attached image.

michele_laino · Answer

I got the same solution! Your answer is right!

anonymous · Answer

Yay! It was killing me trying to get through the book's explanation, but now it seems to have really clicked. Thanks for having a look! :)

michele_laino · Answer

thanks! :)