StringLength["string"] gives the number of characters in a string.

x_y^z is the low-level box representation for x_y^z in notebook expressions.

Through[p[f_1, f_2][x]] gives p[f_1[x], f_2[x]]. Through[expr, h] performs the transformation wherever h occurs in the head of expr.

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. ...

An Euler equation is an ODE of the form The following is an example of an Euler equation. The Legendre linear equation is a generalization of the Euler equation. It has the ...

A linear ordinary differential equation of order n is said to be exact if The condition of exactness can be used to reduce the problem to that of solving an equation of order ...

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is a ...

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...