Solution of exact differential equation

[adam640]

Hi, I'm looking at a past paper for an exam I have on Tuesday and I'm struggling to understand this question on exact derivatives.

Here is a link to the question: http://imageshack.us/photo/my-images/812/questiong.png/

I have looked over my notes for guidance and eventually turned to the solution in the hope that I could work backwards. However I do not understand why half of the equation seems to have disappeared?

Here is the first stage of the solution: http://imageshack.us/photo/my-images/221/solutionp1cvsg.png/

If anyone could help explain to me why this is the case it would be greatly appreciated. I am confident that I would be able to solve the question from here.

Thanks,

Adam

 

[spamiam]

It's just the product rule, where y is a function of x.

$$\frac{d}{dx}(e^{3x}y) = 3e^{3x}y + e^{3x}\frac{dy}{dx}$$