A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...

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

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

DependentVariables is an option which specifies the list of all objects that should be considered as dependent variables in equations that have been supplied.

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

Mathematica 's functions for solving differential equations can be applied to many different classes of differential equations, including ordinary differential equations ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

For most differential equations, the results given by NDSolve are quite accurate. However, because its results are based on numerical sampling and error estimates, there can ...

LinearSolve[m, b] finds an x which solves the matrix equation m.x == b. LinearSolve[m] generates a LinearSolveFunction[...] which can be applied repeatedly to different b.

These "How tos" give step-by-step instructions for common tasks related to solving differential equations in Mathematica .