Mr. Integral
Math notes/Differential Equations/Equations and Initial Values

Initial Values, Existence and Uniqueness — Cheat sheet

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Core rule

Continuous ff gives local existence; local Lipschitz continuity in yy gives uniqueness.

Watch for

For a linear equation y′+p(t)y=q(t)y'+p(t)y=q(t), continuous coefficients on an interval give a unique solution throughout that interval. Divide by the coefficient of y′y' only where it is nonzero.