Here is a step-by-step method for solving them:
1. Substitute y = uv, and
dy/dx = u
dv/dx + v
du/dx
into
dy/dx + P(x)y = Q(x)
2. Factor the parts involving v
3. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
4. Solve using separation of variables to find u
5. Substitute u back into the equation we got at step 2
6. Solve that to find v
7. Finally, substitute u and v into y = uv to get our solution!
I'm so sorry if the explanation is confusing but I hope it's helps you to solve ^ ^
