Find a second-order homogeneous linear ODE for which the given functions are solutions: 1, e^(-2x)?
I have come across this question in my textbook, but have no idea how to solve it. The basis of this wasn't covered in the book. Up to this point in the book, I've just been solving many differential equation. However, this seems to be wanting to work backwards.
I was wondering if anybody knew how to solve it?
The rest of the question is with regard to solving the equation, which I can do simply.
The help is much appreciated.
Best Answer
Hint: $y'' + b y' + c y = 0$ has $e^{r t}$ as a solution if $r$ is a root of the quadratic $r^2 + b r + c = 0$. What quadratic has roots $0$ and $-2$?