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## Homework Statement

From Elementary Differential Equation by Boyce and Diprima

Chapter 2 Miscellaneous Problems #11

(x^2+y)dx + (x+e^x)dy = 0

ANS:(x^3/3)+xy+e^x=c

## Homework Equations

multiplying an integrating factor to make the DE exact:

1. du/dx = u(My - Nx)/ N

2. du/dx = u(Nx-My)/ M

## The Attempt at a Solution

First try: I guessed this can be changed into exact DE so, I tried with the two above equation:

equation 1 gave me:

du/u = e^x/(x+e^x)

I don't know how to solve this...

then equation 2 gave me:

u = e^((e^x)*ln(x^2+y))

I am not sure if multiply this integrating factor to the original DE will make it exact...

Second try: I manipulated the given DE and changed it to a linear form:

dy/dx = -(x^2+y)/(x+e^x)

dy/dx + 1/(x+e^x) * y = (-x^2)/(x+e^x)

and I found integrating factor to be:

I = e^∫1/(x+e^x) dx

which I am unable to solve...