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  3. consider the differential equation y′′

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...

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Electrical Engineering

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)} = _______________________

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