Question

Differential Equations Problem

Solve using Integrating Factors Method

Can you go into detail on how to find the general solution for this problem?
y' – 2y = t^2 e^2t

Answer 1

`y=(t^2e^(2t))/(3)+ce^(2t)`

Explanation:

We have given differential equation
`(dy)/(dt)-2y=t^2e^(2t)`

We know that linear differential equation is given by
`(dy)/(dt)+Py=Q`

On comparing with standard equation P = -2 and Q=
`t^2e^(2t)`

Now integrating factor
`IF=e^(-Pdt)`

`IF=e^(-2dt)=e^(-2t)`

Now solution of differential equation is given by

`y* IF=\int\ IF* Q\ dt`

`y* e^(-2t)=\int\ e^(-2t)* t^2e^(2t)\ dt`

`y* e^(-2t)=(t^2)/(3)+c`

`y=(t^2e^(2t))/(3)+ce^(2t)`