The function powsolve solves a linear differential equation for which initial conditions do not have to be specified.

All the initial conditions must be at zero.

Derivatives are denoted by applying  to the function name. For example, the second derivative of  at 0 is .

The solution returned is a formal power series that represents the infinite series solution.

In some cases, after assigning the name a to the output from the powsolve command, you can enter the command a(_k) to output a recurrence relation for the power series solution.  See examples below.

The command with(powseries,powsolve) allows the use of the abbreviated form of this command.