First-Order ODEs — Separable, Linear, Exact

GRE Math Subject · Axiom Academy

LESSON First-Order ODEs — Separable, Linear, Exact Advanced graduate-level mathematics content Separable differential equations are those where variables can be separated to opposite sides of the equation. Simplify and solve for y implicitly or explicitly Step 2: Linear First-Order Equations Linear first-order ODEs have the form and are solved using an integrating factor. Multiply the equation by to obtain: Compute the integrating factor An equation is exact when it can be expressed as the total differential of some function F(x,y). Solution: Find such that the solution is Integrate M with respect to x: Differentiate with respect to y and match with N to find g(y)

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