This package provides the following functions for solving differential equations.
This loads the package.
A few examples of the use of FOLDSolve:
Here’s an example on which DSolve works for a very long time.
A few examples of the use of BernoulliDSolve:
A few examples of the use of RiccatiDSolve:
The fourth argument is a known solution.
Here’s an example on which DSolve fails.
A few examples of the use of SeparableDSolve:
The equation is given in separated form.
The next example uses the InitialPoint option. Note that the first number is a value for the variable on the left side of the equation and the second number is a value for the variable on the right side of the equation. Here the initial condition is that y = 0 when t = 1.
Since SeparableDSolve returns an equation, it can be combined easily with Solve.
A result from SeparableDSolve is easy to feed into PlotImplicit from the DEGraphics package.
A few examples of the use of SeriesDSolve:
A nonlinear first-order initial-value problem:
A nonlinear second-order initial-value problem:
For a linear second-order equation (with no initial conditions), SeriesDSolve returns partial sums of a pair of “fundamental” solutions, if possible.
Here we get expansions about a point other than 0.
Nonpolynomial coefficients are no problem.
If there is a nonhomogeneous term, SeriesDSolve returns the “rest” solution (i.e., the solution satisfying zero initial conditions).
Complex powers and Frobenius-series solutions are found as well.