Solve a linear ODE by the method of undetermined coefficients
equation; a linear ordinary differential equation
name; the dependent variable
name; the independent variable
The ByUndeterminedCoefficients(ODE, y(x)) command finds the solution of a linear ODE by the method of undetermined coefficients. This method is applicable when the coefficients of y(x) and its derivatives are constant and the forcing function is of a certain form, typically involving polynomials, exponentials, and trigonometric functions. This method works by determining the general form of a particular solution based on the form of the forcing function, substituting the proposed particular solution into the ODE, and solving for the undetermined coefficients.
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 ≔ ⅆ2ⅆx2⁢y⁡x+2⁢ⅆⅆx⁢y⁡x+2⁢y⁡x=sin⁡x
ode2 ≔ ⅆ2ⅆx2⁢y⁡x+4⁢ⅆⅆx⁢y⁡x+4⁢y⁡x=ⅇ−2⁢x
ode3 ≔ ⅆ2ⅆx2⁢y⁡x−4⁢ⅆⅆx⁢y⁡x+4⁢y⁡x=x2
The Student[ODEs][Solve][ByUndeterminedCoefficients] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
The Student[ODEs][Solve][ByUndeterminedCoefficients] 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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