An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.

The general form of an ODE with order n is As in the case of second-order ODEs, such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Chini equations are a generalization of Abel and Riccati equations. This solves a Chini equation.

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...

Automatically selecting between hundreds of powerful and in many cases original algorithms, Mathematica provides both numerical and symbolic solving of differential equations ...

Mathematica's approach to differential operators provides both an elegant and a convenient representation of mathematical structures, and an immediate framework for strong ...