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Differential Equation Solving with DSolve

Introduction to Differential Equation Solving with DSolve

Classification of Differential Equations

Ordinary Differential Equations (ODEs)

Overview of ODEs

Linear Second-Order ODEs

Overview of Linear Second-Order ODEs

Equations with Constant Coefficients

Euler and Legendre Equations

Exact Linear Second-Order Equations

Equations with Solutions Involving Special Functions

Equations with Rational Coefficients

Equations with Non-Rational Coefficients

Inhomogeneous Linear Second-Order Equations

Nonlinear Second-Order ODEs

Higher-Order ODEs

Overview of Higher-Order ODEs

Equations with Constant Coefficients

Euler and Legendre Equations

Exact Equations

Other Types of Higher-Order ODEs

Systems of ODEs

Introduction to Systems of ODEs

Linear Systems of ODEs

Nonlinear Systems of ODEs

Nonlinear ODEs with Lie Symmetries

Partial Differential Equations (PDEs)

Introduction to PDEs

First-Order PDEs

Linear and Quasi-Linear PDEs

Nonlinear PDEs

Second-Order PDEs

Differential-Algebraic Equations (DAEs)

Introduction to DAEs

Examples of DAEs

Initial and Boundary Value Problems

Introduction to Initial and Boundary Value Problems

Linear IVPs and BVPs

Nonlinear IVPs and BVPs

IVPs with Piecewise Coefficients

Working with DSolve—A User's Guide

Introduction

Setting Up the Problem

Verification of the Solution

Plotting the Solution

Generated Parameters

Symbolic Parameters and Inexact Quantities

Is the Problem Well-Posed?

References

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