1 point Find the Laplace Transform of the following expressi

(1 point) Find the Laplace Transform of the following expressions:

Find the Laplace Transform of the following expressions: 7 d^2y/dt^2 - 13 dy/dt - 5y given that y(0) = -6 and dy/dt (0) = 9.

Solution

L(y)=Y

L(dy/dt)=sY-y(0)=sY+6

L(d^2y/dt^2)=s^2Y-sy(0)-y\'(0)=s^2Y+6s-9

Hence, L(7y\'\'-13y\'-5y)

=7(s^2Y+6s-9)-13(sY+6)-5Y

=(7s^2-13s-5)Y+42s-141