As I do my engineering studies, I find more and more ways to solve differential equations, especially the second order ones. With more and more ways to solve these equations, I am loosing my overview and don't know what method to choose now. Which one is the most useful? easiest? most powerful?...
I thought therefore it would be great if this knowledge could be shortly summarized into this post. Myself, I am familiar with three different ways to solve these equations: - the guessing method (with constant coefficients) - Laplace method - the use of Linear Algebra for linear second order differential equations
The best thing to explain this would be to use an example. Therefore, here is one: Solve the (simple) homogeneous differential equation of
Initial conditions: $y(0)=0$ and $y'(0)=1$
Solution: $y=e^t\sin t$
(If you can use a non homogenous example instead to explain methods even further, that would be great)
Thanks a lot for your contribution and help!