solve linear differential equations as power series - Maple Help

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powseries[powsolve] - solve linear differential equations as power series

Calling Sequence

powsolve(sys)

Parameters

sys

-

set or expression sequence containing a linear differential equation and optional initial conditions

Description

• 

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 D to the function name. For example, the second derivative of y at 0 is DDy0.

• 

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.

Examples

withpowseries:

a:=powsolveⅆⅆxyx=yx,y0=1:

tpsforma,x

1+x+12x2+16x3+124x4+1120x5+Ox6

(1)

a_k

a_k1_k

(2)

second system

v:=powsolveⅆ4ⅆx4yx=yx,y0=32,Dy0=12,DDy0=32,DDDy0=12:

tpsformv,x

3212x34x2+112x3+116x41240x5+Ox6

(3)

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