how do you integrate \frac{dy}{dx}=4x-2y.
I don't know if this is right, but this is where I'm going with this:
y'=4x-2y
y'+2y=4x
Solving homogeneous for complementary solution:
y'+2y=0
Solving auxiliary equation:
m+2=0
m=-2
Which gives
y=c_{1}e^{-2x}
y'=-2c_{1}e^{-2x}Now solving original...