# Verify Solution

• Oct 5th 2011, 05:57 AM
moonnightingale
Verify Solution
the book says

Determine for which values of m the function
y=exp(mx) is solution of differential equation

y'' + 6y' + 5y=0

Plz help me
• Oct 5th 2011, 06:31 AM
Soroban
Re: Can u helpmefor this question of differential equations
Hello, moonnightingale!

Quote:

$\displaystyle \text{Determine for which values of }m\text{ the function }y\,=\,e^{mx}$
. . $\displaystyle \text{is solution of differential equation: }\;y'' + 6y' + 5y\:=\:0$

In effect, you are given a differential equation and an answer.
You don't know how to do that?

Differentiate: .$\displaystyle \begin{Bmatrix} y &=& e^{mx} \\ y' &=& me^{mx} \\ y'' &=& m^2e^{mx} \end{Bmatrix}$

Substitute into the differential equation:
. . $\displaystyle m^2e^{mx} + 6me^{mx} + 5e^{mx} \:=\:0$

Divide by $\displaystyle e^{mx}\!:$
. . $\displaystyle m^2 + 6m + 5 \:=\:0$

Can you finish it now?

• Oct 5th 2011, 07:43 AM
HallsofIvy
Re: Can u helpmefor this question of differential equations
It is important to note that $\displaystyle e^{mx}$ is never 0 so you can divide by it.
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