Transform the differential equation

$7y^{\text{'}\text{'}}+58y^{\text{'}\text{'}}-63y^{\text{'}}-522y=9e^{-7t}$

$y^{\text{'}}(0)=0$

$y^{\text{'}}(0)=0$

$y^{\text{'}\text{'}}(0)=1$

into an algebraic equation by taking the Laplace transform of each side. Use $Y$ for the Laplace transform of j $.($net $Y(0)$ i$.$

Therefore

$y=$

$=-\frac{1}{n}+\sqrt[\phantom{2}]{\frac{1}{n}y}+\frac{1}{n+y}$

Taking the inverse Laplace transform we get

$y=$