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

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

unklerhaukus · Answer

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

unklerhaukus · Answer

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