# Thread: Commet on General Solution

1. ## Commet on General Solution

Comment on the statement: The general solution of $\varphi''+6\varphi'+\lambda\varphi=0$ is

$\varphi=C_1\exp(-3+i\sqrt{\lambda-9})+C_2\exp(-3-i\sqrt{\lambda-9})$.

I am not sure what this question wants me to comment about unless it is the fact it should be written like

$\varphi=e^{-3}\left[A\cos(x\sqrt{\lambda-9})+B\sin(x\sqrt{\lambda-9})\right]$

2. When will the solution be a sum of exponential functions?
When will the solution need to have an extra factor of $\displaystyle x$?
When will your solution need to use sines and cosines?