# Finding the general solution of the given differential equation

1. Dec 13, 2013

### bigu01

y"+2y'+y=2e^-t
I tried to find the solution for this nonhomogenous diff. Equation but i could not. First i took a function Y(t)=Ae^-t but i was getting 0=2e^-t.
To get rid of that i took another y'+y=2e^-t and found the solution y=2te^-t + ce^-t. Noticed that first part of this finding is solution of my nonhomogenous diff equation so i took another function Y(t)=Ate^-t but then again i am finding the same answer, i need some tips on how to continue. The general solution for this equation as homogenous equation has repeated roots.

2. Dec 13, 2013

### ShayanJ

When the characteristic equation has repeated roots,the answer is $Ae^{qt}+Bte^{qt}$.
For finding the particular solution,take $y_p=f(t)e^{-t}$ and try finding f(t).

3. Dec 13, 2013

### CAF123

The homogeneous differential equation is second order and so the general solution is composed of two linearly independent pieces. One of those pieces is precisely of the form Y(t) = Ate-t, so subbing this in as a particular solution is redundant. You have to look for another form.

4. Dec 14, 2013

### bigu01

I multiplied my function by t^2, since by multiplying only by t was not working, and it worked.