# Math Help - Integrating Factors method

1. ## Integrating Factors method

Could someone work out how the third equation (43) becomes the fourth equation (44). Seems like magic to me. Where does the K on the Tsub0 term go?

2. ## Re: Integrating Factors method

Just integrate the 3rd equation carefully, you will see

3. ## Re: Integrating Factors method

it's pretty clear that is what I am having trouble with

4. ## Re: Integrating Factors method

lol. When you integrate the 1st term on the RHS, integral of $e^{kt}$ is $e^{kt}/k$ which cancels out the k in the numerator. The integral of the LHS is $ue^{kt}$ itself. The constant c is a constant of integration. First just integrate on both sides and divide both sides by $e^{kt}$. You will arrive at the answer. Hope this helps.