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 ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

RSolve[eqn, a[n], n] solves a recurrence equation for a[n]. RSolve[{eqn_1, eqn_2, ...}, {a_1[n], a_2[n], ...}, n] solves a system of recurrence equations. RSolve[eqn, a[n_1, ...

Apart[expr] rewrites a rational expression as a sum of terms with minimal denominators. Apart[expr, var] treats all variables other than var as constants.

These "How tos" give step-by-step instructions for common tasks related to formatting equations and expressions in Mathematica .

 

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

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 ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

Integrate[f, x] gives the indefinite integral \[Integral]f d x. Integrate[f, {x, x_min, x_max}] gives the definite integral \[Integral]_x_min^x_max\ f\ d x. Integrate[f, {x, ...