Integrating Factor Method
1. Write the linear non-separable differential equation in the form:
dy/dx + p(x)*y = q(x)
2. Find the integrating factor, I:
I = eintegral(p(x) dx)
3. Multiply entire equation by integrating factor. Distribute to each term.
4. Undo product rule. In other words you have: f(x)g’(x) + g(x)f ’(x) and you want to get f(x)
and g(x) back. Note these must be some expressions already in the equation.
5. Integrate both sides. Note you will have [f(x)g(x)] ’ on the left from undoing product rule
so integrating that yields just f(x)g(x)
6. Solve for y, if possible. Solve for + C, if given an initial condition.