Question

A solution of the folowing differential equation is given by $\frac{d^{2}y}{d{x}^2}-5\frac{dy}{dx}+6y=0$

• A. $y=e^{2x}+e^{-3x}$
• B. $y=e^{2x}+e^{3x}$
• C. $y=e^{-2x}+e^{3x}$
• D. $y=e^{-2x}+e^{-3x}$

Answer 1

The correct option is B $y=e^{2x}+e^{3x}$

$\frac{d^{2}y}{d{x}^2}-5\frac{dy}{dx}+6y=0$
$A.E$ is $D^2-5D+6=0$
$D=2,3$
$y=c_1{e}^{2x}+c_2{e}^{3x}$