**DiffEqs `**DETools

This package provides the following functions for solving differential equations.

FOLDSolve[ n]returns the first n terms of
a series expansion about t_{0} of the
solution of a first- or second-order differential
equation. |

Finding solutions of differential equations.

This loads the package.

**FOLDSolve
**

A few examples of the use of FOLDSolve:

Here’s an example on which
DSolve
works for a *very* long time.

**BernoulliDSolve
**

A few examples of the use of BernoulliDSolve:

**RiccatiDSolve
**

A few examples of the use of RiccatiDSolve:

The fourth argument is a known solution.

Here’s an example on which DSolve fails.

**SeparableDSolve
**

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.

**SeriesDSolve
**

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.

Converted by