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jaredogden
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Homework Statement
find the general solution using integrating factors.
xy' - 2y = 3x
Homework Equations
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!
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