1. The problem statement, all variables and given/known data find the general solution using integrating factors. xy' - 2y = 3x 2. Relevant equations 3. The attempt at a solution x(dy/dx) = 3x + 2y x*dy = (3x + 2y)dx (-3x + 2y)dx + xdy = 0 My = -3x + 2 Nx = 1 Not Exact (hence the use of integrating factors) μ(x)(-3x + 2y)dx + μ(x)xdy = 0 Differentiating with respect to y for M and x for N μ(x)(-3x + 2) = μ'(x)x + μ(x) trying to simplify -3xμ(x) + 2μ(x) - μ(x) = μ'(x) -3xμ(x) - μ(x) = μ'(x) -μ(x)(3x - 1) = μ'(x) I know I need to solve for μ(x) to multiply M and N by, I am not sure if I have done everything correct up until now. I assume that I possibly just need a little help with the algebra to be able to set up an integral to solve for μ(x) but I am not sure. Any help would be greatly appreciated, I'm not sure if I missed something from the beginning or am almost there. Thanks ahead of time!