Solving a Nonlinear Differential Equation with Variable Coefficients

[iamtrojan3]

Homework Statement

this problem was on my finals and i stared at it for 30 mins straight and still didn't figure it out and now it just bothers me that i don't know how to do the first problem on my final exam.

"find the general solution to the dfq"
xy'+xy= 1-y

Homework Equations

The Attempt at a Solution

i don't think its linear cause if you do the integrating factor the right side is interms of x and y
i don't think its separable... or multiplying by 1/x and subbing v for y/x could help
i don't think its exact? or is it I am not sure
bernouli's formula won't help here.
i don't know its probably something really stupid and easy... thanks for the help!

 

[Dick]

The y doesn't have to be on the right side. Write it as x*y'+(x+1)*y=1. Now divide by x and find the integrating factor.

 

[iamtrojan3]

OH MY GOD. there goes 20 points that i should of gotten. thank you for the helpe.