Hi again, here's another question that I had a go at but haven't got any answers for, does the working and answer seem ok?

Solve

The method I use is outlined in my lecture notes, however I am unsure of it's actual name.

First thing I did was to isolate the x term on the right hand side by multiplying everything by

, giving the equation

I then use the substitution of

, then differentiate this equation with respect to x and you get

.

Placing these two substitutions into my original equation this simplifies to be

.

I wasn't too sure what to do at this point, I took a guess at using an integrating factor of

, which when I put back into the equation gave me

.

This then integrates to

, which after putting back in my substitution gave the answer of

.

Is any of this correct, or know me have I made an early error and then just answered a completely different question?

Thanks again

Craig