In: Electrical Engineering
Consider the
differential equation
y′′(t)+15y′(t)+56y(t)=−210exp(-1t),
with initial conditions y(0)=−14, and
y′(0)=72.
A)Find the Laplace transform of the solution 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)} = _______________________