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