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  3. consider the differential equation y′(t)+9y(

Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t), with initial condition y(0)=4, A)Find the Laplace transform of the solution Y(s).Y(s). Write the...

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Advance Math

Consider the differential equationy′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,

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

Y(s)= ______________

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

Y(s)= ____ + ______ +______

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

L−1{Y(s)} = _______________________

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