Separation of Variables

AP Calculus · Axiom Academy

Lesson Separation of Variables The primary technique for solving first-order DEs on the AP exam A DE is separable if it can be written as — a product of a function of x alone and a function of y alone. Use initial conditions to find C Solve for y : y = Ae^ x^2/2 where A = e^C Apply IC: 3 = Ae^0 = A , so y = 3e^ x^2/2 Separation works when the DE factors as g(x)h(y) Don t forget the +C after integrating — or use |y| properly Always check if h(y)=0 creates an equilibrium solution This is the most tested DE technique on the AP exam

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