Question

Consider the differential equation y′′(t)+4y′(t)+5y(t)=74exp(−8t),
with initial conditions y(0)=12, and y′(0)=−44.

A)Find the Laplace transform of the solution Y(s).Y(s). Write the solution as a single fraction in s.

Y(s)= ______________

B) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form (c/(s-p)), where c is a constant and the root p is a constant. Both c and p may be complex.

Y(s)= ____ + ______ +______

C) Find the inverse transform of Y(s). The solution must consist of all real terms.

L−1{Y(s)} = _______________________

Answer 1