Does an initial-value problem have a solution, and is that solution the only one? This complete Woody Calculus lesson explains the existence and uniqueness theorem, the rectangle test, worked examples, nonunique solutions, finite-time blow-up, maximal intervals, the nonintersection principle, and higher-order linear ODEs.
Slope fields make differential equations visible. Learn how to construct and read direction fields, use isoclines, sketch IVP solution curves, distinguish zero-slope curves from equilibria, understand uniqueness, analyze logistic stability, and apply Euler’s method through exact worked examples.
Euler’s method approximates the solution of an initial-value problem by repeatedly using the differential equation’s slope. Learn the update formula, complete a worked example, compare step sizes, and verify the approximation against an exact solution.