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 ...

A Bernoulli equation is a first-order equation of the form The problem of solving equations of this type was posed by James Bernoulli in 1695. A year later, in 1696, G. ...

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

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

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 ...

Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give ...

Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...

RiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the continuous algebraic Riccati equation ConjugateTranspose[a].x + x.a - ...

Equations Solving Equations The Representation of Equations and Solutions

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