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

Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...

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 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 ...

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 ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

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 ...

An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.