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Property of differential equations describing physical phenomena Differential equations Scope Fields Natural sciencesEngineering Astronomy Physics Chemistry Biology Geology Applied mathematics Continuum mechanics Chaos theory Dynamical systems Social sciences Economics Population dynamics Classification Types Ordinary Partial Differential-algebraic Integro-differential Fractional Linear Non-linear By variable type Dependent and independent variables Autonomous Coupled / Decoupled Exact Homogeneous / Nonhomogeneous Features Order Operator Notation Relation to processes Difference (discrete analogue) Stochastic Stochastic partial Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya theorem General topics Initial values Boundary values Dirichlet Neumann Robin Cauchy Periodic Wronskian Abel's identity Sturm–Liouville theory Floquet theory Phase portrait Stability Lyapunov Asymptotic Exponential Series solutions Rate of convergence Asymptotic series Special functions Numerical integration Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite element Infinite element Finite volume Galerkin Petrov–Galerkin Green's function Integrating factor Integral transforms Perturbation theory Reduction of order Runge–Kutta Separation of variables Undetermined coefficients Variation of parameters WKB approximation People List Newton Leibniz Jacob Bernoulli d'Alembert Clairaut Euler Lagrange Laplace Wroński Fourier Cauchy Green Dirichlet Sturm Liouville Neumann Robin Boole Kovalevskaya Runge Kutta Lipschitz Lindelöf Picard Jeffreys Nicolson Crank Hrennikoff Courant Named equationsvte In mathematics, the solution to a well-posed problem satisfies the following properties: It exists; It is unique; Its behavior changes continuously with the auxiliary conditions, such as initial or boundary values.

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