When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

Solving equations involving power series. Here is a power series. This gives an equation involving the power series.

Chini equations are a generalization of Abel and Riccati equations. This solves a Chini equation.

A Clairaut equation is a first-order equation of the form A remarkable feature of this nonlinear equation is that its general solution has a very simple form. This is an ...

f' represents the derivative of a function f of one argument. Derivative[n_1, n_2, ...][f] is the general form, representing a function obtained from f by differentiating n_1 ...

[1] Butcher, J. C. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods. John Wiley and Sons, 1987. [2] Iserles, A. A First ...

Mathematica is widely used throughout the world for precollege education, in mathematics and many other fields. This page lists a few Mathematica functions used particularly ...

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

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 ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.