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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.
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