  Solve y”+2y’+y=e^t using a power series, please show all your work and show that the answer is equivalent to c1e^-t +c2te^-t +e^t/4 once you get to the part where you have the series expansion please explain to me how you convert them into the closed form so everything makes sense to me .

Question

Solve y”+2y’+y=e^t using a power series, please show all your work and show that the answer is equivalent to c1e^-t +c2te^-t +e^t/4
once you get to the part where you have the series expansion please explain to me how you convert them into the closed form so everything makes sense to me .

Step 1

To develop the power series solution for the given differential equation

Step 2

Assume the power series solution y(t) in the form specified (in view of e^t on the right hand side)

Step 3

In order to find the coefficients , substitute the power series y(t) in the diff...

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Differential Equations 