Not sure about this one, a quick check would be appreciated and a bit of help as to where I've gone wrong if it's not right... a friend got a different answer so I'm questioning my own.
subject to y(0) = 1 and y'(0) = -1
Testing y(0) there does get me 1 so it seems right to me...
I think there's a problem here. If you want the solution subject to the following IC's, , then the solution you give is right (with a slight change- should be ). However, if you want the solution with the IC's you give , I believe the correct solution is
edit: Ah, I missed a negative sign when working out y'(0)... stupid mistake heh. All fixed now.