Basic plotting functions. This plots a graph of sin(x) as a function of x from 0 to 2π. You can plot functions that have singularities. Mathematica will try to choose ...

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. ...

Mathematica has many powerful features which enable you to solve many kinds of equations.

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 ...

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 ...

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 ...

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 ...

Unicode: F74B. Alias: Esc DD Esc. Compound operator.  can only be interpreted by default when it appears with ∫ or other integral operators. Used in mathematics to indicate ...

BesselJ[n, z] gives the Bessel function of the first kind J_n (z).

It may happen that a given ODE is not linear in y(x) but can be viewed as a linear ODE in x(y). In this case, it is said to be an inverse linear ODE. This is an inverse ...