Further Examples: DSolve
Here is the solution to a second order ordinary differential equation. It uses C and C as the constants of integration by default.
This solves the same equation, specifying that the integration constants are K and K.
You can add constraints and boundary conditions for differential equations.
This verifies the solution.
Here is the solution for a Riccati-type equation.
Here is the solution for an Abel-type equation.
Here is the solution for a more general Abel-type equation. K$ variables are used as dummy integration variables.
Here is an equation whose solution involves Mathieu functions.
Solving this equation uses a combination of methods for rational, exponential, and special function solutions, as well as reduction of order.
For this equation, DSolve returns an implicit solution.
The solution of this equation involves products of Airy functions.
When the initial or boundary conditions are given at singularities, DSolve uses Limit internally.
This equation has missing variables.
The arguments of the dependent variable in differential equations should match the independent variables literally.