4B_HO1_IntegratingFactor.pdf - MATH 4B Integrating Factor...

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MATH 4B Integrating Factor Method (for 1st order linear ODE’s) Step 1: Write the equation in standard form: dy dx + p ( x ) y = g ( x ) , (1) so that you can identify p and g . Step 2: Calculate the integrating factor μ (pronounce “mu”): μ = e R p ( x ) dx . Step 3: Multiply μ to both sides of equation (1), and after some simplifications (omitted here), ( μy ) 0 = μg. (2) Step 4: Integrate both sides of equation (2) (Pro tip: Don’t forget the constant of integration!), then divide both sides by μ and solve for y . Practice Problems Problem 1. Find the general solution to the equation:
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