Solve ODE using method of integrating factors.

[alias25]

Homework Statement

solve the following equation using method of intergrating factors:

Homework Equations

dy/dx = y + cosx - sinx

The Attempt at a Solution

i think i have to get it in the form dy/dx + r(x)y = f(x)

but i can't see how,

if i multiply or divide by a factor i won't have dy/dx on its own. and how do i identify what's f(x) and r(x)?

i also tried

dy + (-y -cosx +sinx)dx = 0

and then just finding a factor to make it an exact differntial, but I am not sure how i determine the factor.

 

[drpizza]

simply subtract the y from both sides...
dy/dx -y = cosx - sinx

your function in front of y is simply a constant function (-1)

 

[tim_lou]

its kinda obvious that y=sin(x) is a solution...