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Mathematica 9 (2012)

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Virtual Book > Mathematics and Algorithms > Differential Equation Solving with DSolve
MATHEMATICA OVERVIEW

Differential Equation Solving with DSolve

Introduction to Differential Equation Solving with DSolve

Classification of Differential Equations

Ordinary Differential Equations (ODEs)Ordinary Differential Equations (ODEs)

Overview of ODEs

First-Order ODEsFirst-Order ODEs

Straight Integration

Separable Equations

Homogeneous Equations

Linear Equations

Inverse Linear Equations

Bernoulli Equations

Riccati Equations

Exact Equations

Clairaut Equations

Abel Equations

Chini Equations

Linear Second-Order ODEsLinear 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 ODEsHigher-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 ODEsSystems of ODEs

Introduction to Systems of ODEs

Linear Systems of ODEs

Nonlinear Systems of ODEs

Nonlinear ODEs with Lie Symmetries

Partial Differential Equations (PDEs)Partial Differential Equations (PDEs)

Introduction to PDEs

First-Order PDEsFirst-Order PDEs

Linear and Quasi-Linear PDEs

Nonlinear PDEs

Second-Order PDEs

Differential-Algebraic Equations (DAEs)Differential-Algebraic Equations (DAEs)

Introduction to DAEs

Examples of DAEs

Initial and Boundary Value ProblemsInitial 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 GuideWorking 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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