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Student[ODEs][Solve]

  

BySeries

  

Find a series solution for a linear homogeneous ODE with polynomial coefficients

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

BySeries(ODE, y(x))

Parameters

ODE

-

an ordinary differential equation

y

-

name; the dependent variable

x

-

name; the independent variable

Description

• 

The BySeries(ODE, y(x)) command finds a particular series solution of a linear homogeneous ODE with polynomial coefficients.

• 

Note that the series solution may not represent the complete solution of the given ODE.

Examples

withStudentODEsSolve:

ode1diffdiffyx,x,x+xdiffyx,x+yx=0

ode1ⅆ2ⅆx2yx+xⅆⅆxyx+yx=0

(1)

BySeriesode1,yx

yx=k=0akxk,ak+2=akk+2

(2)

ode3x2diffyx,x,x+x2diffyx,x+x36yx=0

ode3x2ⅆ2ⅆx2yx+x2ⅆⅆxyx+x36yx=0

(3)

BySeriesode3,yx

yx=k=0akxk+3,ak+3=kak+2+ak+5ak+2k+8k+3,a1=a02,a2=a07

(4)

ode4diffyx,x,x+diffyx,x+x2yx=0

ode4ⅆ2ⅆx2yx+ⅆⅆxyx+x2yx=0

(5)

BySeriesode4,yx

yx=k=0akxk,ak+4=kak+3+ak+3ak+3k2+7k+12,a2=a12,a3=a16

(6)

ode5diffx2+1diffyx,x,x+12yx=0

ode52xⅆⅆxyx+x2+1ⅆ2ⅆx2yx+12yx=0

(7)

BySeriesode5,yx

yx=a032x52x3

(8)

ode6diffyx,x,x=sinxyx

ode6ⅆ2ⅆx2yx=sinxyx

(9)

BySeriesode6,yx

Error, (in Student:-ODEs:-SeriesSolve) series solutions are only available for linear homogeneous ODEs with polynomial coefficients

Compatibility

• 

The Student[ODEs][Solve][BySeries] command was introduced in Maple 2021.

• 

For more information on Maple 2021 changes, see Updates in Maple 2021.

See Also

dsolve

MultiSeries

series

Student

Student[ODEs]

Student[ODEs][Solve]

Sum