Consider thedifferential equationy′′(t)+15y′(t)+56y(t)=−210exp(-1t),
with initial conditions y(0)=−14, andy′(0)=72.
A)Find the Laplacetransform of the solution Y(s). Write thesolution as a single fraction in s.
Y(s)=______________
B) Find the partialfraction decomposition of Y(s). Enter all factors as first orderterms 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. Bothc and p may be complex.
Y(s)= ____ + ______+______
C) Find the inversetransform of Y(s). The solution must consist of all real terms.
L−1{Y(s)} = _______________________
