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.

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 ...

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 ...

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 ...

While DSolve usually returns the correct solution to a differential equation it is given, it is common practice to verify the solution returned by any differential equation ...

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

There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

Mathematica's symbolic character allows it to provide deep integrated support for algebraic numbers. At the core are Root objects, which provide exact implicit ...