A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004. [A89] Abramov, S. A. "Rational Solutions of Linear ...

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 ...

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.

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

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 ...

The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

This equation is solved by simply integrating the right-hand side with respect to x. Here is a plot of the integral curves for different values of the arbitrary constant C[1].

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...