Solve a system of first order linear ODEs by the method of variation of parameters
ByVariationOfParameters(A, F, x)
list, set, or equation; a system of first order linear ordinary differential equations
list or set or Vector of functions; the solving variables
Matrix; the Matrix of coefficients
Vector; the Vector of forcing functions
name; the independent variable
The ByVariationOfParameters(SYS, vars) command finds the solution of a system of first order linear ODEs using variation of parameters.
The system SYS may be written as a list or set of ODEs. If the solving variables cannot be unambiguously determined from the form of SYS, Y must also be specified as a list or set containing the solving variables.
Alternatively, SYS may be written as a single equation of the form:
where Y is a Vector of solving variables, DY a Vector of their derivatives, A is the Matrix of coefficients, and F is the Vector of forcing functions. In this case, Y does not need to be specified as an extra argument since it can be determined from the form of SYS.
A third syntax: ByVariationOfParameters(A, F, x) is also available as a shortcut to the above syntax DY = A . Y + F.
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.
A ≔ Matrix⁡1,2,3,2
F ≔ 1,ⅇx
Y ≔ y1⁡x,y2⁡x:
sys1 ≔ ∂∂x⁢Y=`.`⁡A,Y+F
sys2 ≔ seq⁡∂∂x⁢Yi=`.`⁡A,Y+Fi,i=1..2
sys3 ≔ convert⁡sys2,set
The Student[ODEs][Solve][ByVariationOfParameters] command was introduced in Maple 2022.
For more information on Maple 2022 changes, see Updates in Maple 2022.
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