Ans8-1

Taking Laplace transform of both sides gives:

(since y(0) = 0)

Solving for Y and finding the partial fraction decomposition gives:

MATH

$s=-1\qquad$ gives $3=10A\qquad$ gives $A=\dfrac{3}{10}$

$s=0\qquad$ gives $3=9A+C\qquad$ gives $C=\dfrac{3}{10}$

$s=1\qquad$ gives $3=10A+2B+2C\qquad$ gives $B=-\dfrac{3}{10}$

MATH

Finding the inverse Laplace tranform gives us the solution for y as a function of t:

$\sin 3t$