Math Problem Solver

In this exercise we will use the Laplace transform to solve the following initial value problem:

y′′+25y={25,0,0≤t<22≤t,}y(0)=−3,y′(0)=−15

(1) First, using Y

for the Laplace transform of y(t)

, i.e., Y=L(y(t))

, find the equation obtained by taking the Laplace transform of the initial value problem

(s^(2)+25)Y+3s+15

=

(25/s)-(25e^(-2s)/s)

(2) Next solve for Y=

((25/s)-(25e^(-2s)/s)-3s-15)/(s^(2)+25)

(3) Finally apply the inverse Laplace transform to find y(t)

y(t)=