dy/dx + P(x) = Q(x)
This is the correct initial form. Convert to this form if necessary.
Next find the integrating factor ∫ Pdx.
e
Then Multiply everything by this factor and verify that left side is product rule.
Integrate both sides.
Solve for y
Note sometimes an equation will be exact - that is the left side will be the product rule already so there is no need to employ the integrating factor in this case.
