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differential-equations

Linear vs. nonlinear differential equations

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Local knowledge map

Local knowledge map

$n$th-order linear equations Classifying second-order PDEs: the discriminant test Deriving the heat equation Deriving the wave equation Linear independence of two functions Ordinary points and the power-series method Solving linear first-order PDEs by characteristics The linear differential operator L The superposition principle for linear PDEs Writing a first-order system in matrix form Order, linearity, and homogeneity of a PDE Second-order linear equations, standard form Linear vs. nonlinear differential equations Building a differential equation from a word… Exact differential equations Existence and uniqueness (the Picard-Lindelof… Explicit vs. implicit solutions Hooke's law and the spring restoring force Separable differential equations Slope fields Why a closed-form solution isn't always available Writing a system in matrix form What a differential equation is (order, solutions, general vs… Chain rule for derivatives

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