How to solve first-order linear ordinary differential equation?

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.