Question

Using Y for the Laplace Transform of y(t), find the equation that you get by taking the Laplace transform of the differential equation and solve for Y(s). y"+25y= 8t, 0<=t<=4 32, t>4 initial conditions y(0)=0 y'(0)=0

Answer 1

\[y''+25y= \begin{cases} 8t,& 0\leq t\leq4 \\ 32,&t>4 \end{cases}\]

Answer 2

first , can you express the piecewise function as a single expression using the heaviside step unit function?