To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

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 ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

The functionality of Calculus`DSolveIntegrals` is now available in the built-in Mathematica kernel function DSolve.

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 ...

DSolve can be used for finding the general solution to a differential equation or system of differential equations. The general solution gives information about the structure ...

 

Mathematica 's functions for solving differential equations can be applied to many different classes of differential equations, including ordinary differential equations ...

Mathematica 's differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms ...