Student[ODEs][Solve]
BySeries
Find a series solution for a linear homogeneous ODE with polynomial coefficients
Calling Sequence
Parameters
Description
Examples
Compatibility
BySeries(ODE, y(x))
ODE
-
an ordinary differential equation
y
name; the dependent variable
x
name; the independent variable
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.
with⁡StudentODEsSolve:
ode1≔diff⁡diff⁡y⁡x,x,x+x⁢diff⁡y⁡x,x+y⁡x=0
ode1≔ⅆ2ⅆx2y⁡x+x⁢ⅆⅆxy⁡x+y⁡x=0
BySeries⁡ode1,y⁡x
y⁡x=∑k=0∞⁡ak⁢xk,ak+2=−akk+2
ode3≔x2⁢diff⁡y⁡x,x,x+x2⁢diff⁡y⁡x,x+x3−6⁢y⁡x=0
ode3≔x2⁢ⅆ2ⅆx2y⁡x+x2⁢ⅆⅆxy⁡x+x3−6⁢y⁡x=0
BySeries⁡ode3,y⁡x
y⁡x=∑k=0∞⁡ak⁢xk+3,ak+3=−k⁢ak+2+ak+5⁢ak+2k+8⁢k+3,a1=−a02,a2=a07
ode4≔diff⁡y⁡x,x,x+diff⁡y⁡x,x+x2⁢y⁡x=0
ode4≔ⅆ2ⅆx2y⁡x+ⅆⅆxy⁡x+x2⁢y⁡x=0
BySeries⁡ode4,y⁡x
y⁡x=∑k=0∞⁡ak⁢xk,ak+4=−k⁢ak+3+ak+3⁢ak+3k2+7⁢k+12,a2=−a12,a3=a16
ode5≔diff⁡−x2+1⁢diff⁡y⁡x,x,x+12⁢y⁡x=0
ode5≔−2⁢x⁢ⅆⅆxy⁡x+−x2+1⁢ⅆ2ⅆx2y⁡x+12⁢y⁡x=0
BySeries⁡ode5,y⁡x
y⁡x=a0⁢32⁢x−52⁢x3
ode6≔diff⁡y⁡x,x,x=sin⁡x⁢y⁡x
ode6≔ⅆ2ⅆx2y⁡x=sin⁡x⁢y⁡x
BySeries⁡ode6,y⁡x
Error, (in Student:-ODEs:-SeriesSolve) series solutions are only available for linear homogeneous ODEs with polynomial coefficients
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]
Sum
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