Mathematica 's differential equation solving functions can be applied to many classes of differential equations, automatically selecting the appropriate algorithms without ...

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

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 ...

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

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].

C[i] is the default form for the i\[Null]\[Null]^th parameter or constant generated in representing the results of various symbolic computations.

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 ...

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 ...

The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...