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In: Advanced Math

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...

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 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)} = _______________________

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Expert Solution

Colby Messinger answered 2 years ago
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