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Consider the differential equation y”+5y’+6y=f(t). Write the form of the particular solution if f(t) is the...

Consider the differential equation y”+5y’+6y=f(t). Write the form of the particular solution if f(t) is the following. Do not solve.

(a) f(t)= 5t*e^(-2t)

(b) f(t)= t^2*sin(2t)

(c) f(t)= t + 1

(d) f(t)= 2t^2*e^(-3t)

(e) f(t)= 4t^2+3t
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