Deserted Land

文章目录Second Order EquationsDefinitionsSecond-Order Differential EquationSolutionLinear EquationsExistence and UniquenessStructure of General SolutionsLinear CombinationLinear IndependentGeneral Solutio...

文章目录1. Separable Differentiable Equations2. Linear EquationsFirst-order linear equationSolution of the homogeneous equationSolution of the inhomogeneous equationAn alternate solution -- Variation of p...

Differential Equations and SolutionsOrdinary Differential EquationsAn ordinary differential equation is an equation involving an unknown function of a single variable together with one or more of it...

ODE – Autonomous Equations and StabilityAutonomous Equationis an equation of the special formx′=f(x)(1)x'=f(x) \qquad (1)x′=f(x)(1)Note: 可以看出这个方程于函数x(t)x(t)x(t)的自变量ttt无关Direction field因为与自变量无关...

文章目录ODE -- Existence and Uniqueness of Solutions, Dependence of Solutions on Initial ConditionsTheorem: Existence of SolutionsTheorem: Uniqueness of solutionsTheorem: Estimation of Difference of Two S...