Sir,

while solving a differential equation problem

I got the equation as y/(x+1) = integration of e^{3x}(x + 1) + c (integration constant)

what I did in the integration I multiplied and divided by 3

3e^{3x}(x + 1)

_________

3

e^{3x}(3x + 3) I took f(x) = 3x and f'(x) = 3]

_________

3

I used integration of e^{x }[f(x) + f'(x)]

= e^{x }f(x) + c

= xe^{x}+ c

---

3

But they have solved the problem by using parts

They get a different answer.

e^{3x}(x + 2)

_________ + c

9

Kindly explain were I went wrong?

with regards,

Aranga