Exponential equation:

Inhomogeneous first-order equation:

Solve a boundary value problem:

Plot the solution:

Second-order equation with constant coefficients:

Cauchy-Euler equation:

Second-order equation with variable coefficients, solved in terms of elementary functions:

Airy's equation:

Spheroidal equation:

Equations with nonrational coefficients:

Higher-order equations:

Solution in terms of hypergeometric functions:

Fourth-order equation solved in terms of Kelvin functions:

Using a piecewise forcing function:

A differential equation with a piecewise coefficient:

A nonlinear piecewise-defined differential equation:

Differential equations involving generalized functions:

A simple impulse response or Green's function:

Solve a Riccati equation:

Implicit solution for an Abel equation:

Homogeneous equation:

Solution in terms of

WeierstrassP:

Solution in terms of hyperbolic functions:

Diagonal linear system:

Inhomogeneous linear system with constant coefficients:

Nonlinear system:

Solve a system of linear differential-algebraic equations:

Solve a boundary value problem:

An index-2 differential-algebraic equation:

General solution for a linear first-order partial differential equation:

The solution with a particular choice of the arbitrary function

C:

General solution for a quasilinear first-order partial differential equation:

Complete integral for a nonlinear, first-order Clairaut equation:

Initial value problem for a linear first-order partial differential equation:

Linear second-order partial differential equation with constant coefficients:

Traveling wave solution for the Korteweg-de Vries (KdV) equation: