Find a series solution for a linear homogeneous ODE with polynomial coefficients
an ordinary differential equation
name; the dependent variable
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.
Use the option output=steps to make this command return an annotated step-by-step solution. Further control over the format and display of the step-by-step solution is available using the options described in Student:-Basics:-OutputStepsRecord. The options supported by that command can be passed to this one.
ode1 ≔ ⅆⅆx⁢ⅆⅆx⁢y⁡x+x⁢ⅆⅆx⁢y⁡x+y⁡x=0
ode3 ≔ x2⁢ⅆ2ⅆx2⁢y⁡x+x2⁢ⅆⅆx⁢y⁡x+x3−6⁢y⁡x=0
ode4 ≔ ⅆ2ⅆx2⁢y⁡x+ⅆⅆx⁢y⁡x+x2⁢y⁡x=0
ode5 ≔ ⅆⅆx⁢−x2+1⁢ⅆⅆx⁢y⁡x+12⁢y⁡x=0
The BySeries command accepts only linear homogeneous ODEs with polynomial (or rational polynomial) coefficients. Attempting to use it for an ODE not of this form results in an error message.
ode6 ≔ ⅆ2ⅆx2⁢y⁡x=sin⁡x⁢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.
The Student[ODEs][Solve][BySeries] command was updated in Maple 2022.
The output option was introduced in Maple 2022.
For more information on Maple 2022 changes, see Updates in Maple 2022.
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