Use an integrating factor to solve

1. Feb 23, 2014

Calu

1. The problem statement, all variables and given/known data

Use an integrating factor to determine the general solutions of the following differential
equation:

dx/dt - 2/t = 2t3 + (4t2)(e4t)

2. Relevant equations

R(x) = e∫P(x).dx

3. The attempt at a solution

Usually the equation is in the form dx/dt + P(x)t = Q(x) but here I'm not sure what to do to find P(x) here as I have 1/t, t3 and t2.

I'm also not sure how to go about finding a solution either. I know that once I have found the integrating factor, I have to multiply the original equation by R(x). After that I'm not sure what to do.

2. Feb 23, 2014

jackarms

Well, it looks like this equation is actually separable. Just move the -2/t over, and the right side will be entirely a function of t.

3. Feb 23, 2014

Calu

I realised that whilst I was doing it, but the question specifically asks me to use an integrating factor. thanks for the reply though.

4. Feb 23, 2014

LCKurtz

Here, your independent variable is $t$. So your integrating factor is $R=e^{\int\frac 2 t~dt}$. Evaluate that and multiply through by it.

5. Feb 23, 2014

Calu

Oh, I see. Thanks, I was being a bit stupid there.