$x^{}+2x=t{e}^{-3t}sin5t,x(0)=x^{}(0)=0$

Multiple Choice

$x(t)=\frac{5}{338}{e}^{-3t}+\frac{e^{-2t}}{338}(65tcos5t+13tsin5t-12sin5t+5cos5t)$

$x(t)=\frac{5}{338}{e}^{-3t}-\frac{e^{-2t}}{338}(65tcos5t+13tsin5t-12sin5t+5cos5t)$

$x(t)=\frac{5}{338}{e}^{-2t}+\frac{e^{-3t}}{338}(65tcos5t+13tsin5t-12sin5t+5cos5t)$

Required information

Consider the following model:

$x^{}=-4x+2y+f(t)$

$y^{}=-9y-5x+g(t)$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

$f(t)=g(t)=0,$ how long will it take for the free responses $x(t)$ and $y(t)$ to essentially disappear?

will take $$ seconds for the responses to disappear.

Required information

Consider the following model:

$x^{}=-4x+2y+f(t)$

$y^{}=-9y-5x+g(t)$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

$f(t)=g(t)=0,$ how long will it take for the free responses $x(t)$ and $y(t)$ to essentially disappear?

will take $$ seconds for the responses to disappear.

Required information

Consider the following model:

$x^{}=-4x+2y+f(t)$

$y^{}=-9y-5x+g(t)$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

$f(t)=g(t)=0,$ how long will it take for the free responses $x(t)$ and $y(t)$ to essentially disappear?

will take $$ seconds for the responses to disappear.