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

Printable View

- Oct 5th 2011, 05:57 AMmoonnightingaleVerify 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 AMSorobanRe: 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 are asked to check the 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 AMHallsofIvyRe: 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.