# Integrating factor confusion

1. Sep 19, 2009

### iamtrojan3

1. The problem statement, all variables and given/known data
Solving this differential equation
ty' + 2y = t^2 - t + 1

2. Relevant equations
Its linear so i set it up in linear form
y' + y(2/t) = t - 1 +1/t

3. The attempt at a solution

the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)...
Here's the question, my book says u = t^2, and i just can't figure out how e ^ integral (2dt/t) is t^2

Its probably some stupid thing that i'm getting stuck on, thanks.
I know how to do this afterwards, i just can't for the life of god figure out why u = t^2

2. Sep 19, 2009

### Bohrok

$$u = e^{\int\frac{2dt}{t}} = e^{2\ln t} = (e^{\ln t})^2$$

3. Sep 19, 2009

### iamtrojan3

oh wow i thought u could bring the 2 out front.... thanks for clearing that up

4. Sep 19, 2009

### CFDFEAGURU

Thanks Bohrok, I thought that was were is was coming from also but was having trouble typing it out.

Matt

Last edited: Sep 19, 2009