hrostentsp6

2021-11-11

Solve the initial value problem below using the method of laplace transforms.

Himin1945

Taking Laplace transforamtion on both sides
$L\left\{y{}^{″}\right\}+2L\left\{{y}^{\prime }\right\}-3L\left\{y\right\}=0$
Laplace transformation derivatives define
$L\left\{y\right\}=\frac{s+11}{{s}^{2}+25-3}$
$=\frac{5+11}{\left(s-1\right)\left(s+3\right)}$
$L\left\{y\right\}=\frac{3}{s-1}-\frac{2}{s+3}$
$y\left(t\right)=3{e}^{t}-2{e}^{-3t}$

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