# Math Help - Differential Equations

1. ## Differential Equations

Determine for which values of m the function $\phi(x) = e^{mx}$ is a solution to the given equations:

(a) $\frac{d^2y}{dx^2} + 6\frac{dy}{dx} + 5y = 0$

(b) $\frac{d^3y}{dx^3} + 3\frac{d^2y}{dx^2} + 2\frac{dy}{dx} = 0$

2. Just try them.
$m^2 e^{mx}+6m e^{mx} + 5 e^{mx}=0$
Solve for m $m^2 +6m + 5 =0$
$m =\frac{-6\pm \sqrt{36-4\cdot 5}}{2} = \frac{-6\pm 4}{2}= -3 \pm 2$
For the next number we have $m(m+1)(m+2)=0$