GenerateSimilarODE - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

RandomTools

  

GenerateSimilarODE

  

create a random differential equation similar to the one given

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GenerateSimilarODE( eqn )

Parameters

eqn

-

differential equation with one dependent and one independent variable

Description

• 

The GenerateSimilarODE command takes an ordinary differential equation (ODE) eqn with 1 dependent and 1 independent variable and returns a similar ODE in the same variables.

• 

Linear ordinary differential equations with constant coefficients that have order higher than 1 return a linear ordinary differential equations with constant coefficients that have similar roots to the characteristic polynomial of the ODE. Each real root in eqn will have a corresponding real root in the output ODE, each repeated root in eqn will correspond to a repeated root in the output ODE. A pair of complex conjugate roots in eqn will correspond to a pair of complex conjugate roots in the output ODE.

• 

Linear ordinary differential equations with constant coefficients that have order higher than 1 and a forcing function that contains functions that are linearly dependent to the solution of the homogeneous ODE produce an ODE with the similar roots described above and a forcing function that has functions that are linearly dependent to the solutions of the homogeneous output ODE.   

• 

Bessel differential equations or differential equations that can be converted into Bessel differential equations return Bessel differential equations or differential equations that can be converted into Bessel differential equations.

• 

Differential equations that when solved produce terminating Legendre polynomials return differential equations that when solved produce terminating Legendre polynomials.

• 

Differential equations that when solved produce terminating Laguerre polynomials return differential equations that when solved produce terminating Laguerre polynomials.

• 

Chebyshev differential equations produce Chebyshev differential equations.

Examples

(1)

(2)

2nd order linear ODE with constant coefficients with a characteristic polynomial that has real roots.

(3)

(4)

(5)

(6)

2nd order linear ODE with constant coefficients with a repeated root.

(7)

(8)

(9)

(10)

2nd order linear ODE with a pair of complex conjugate roots.

(11)

(12)

(13)

(14)

2nd order linear ODE with forcing function that contains a function that is linearly dependent to a solution to the homogeneous ODE.

(15)

(16)

(17)

(18)

Bessel differential equation.

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

ODEs that can be converted to a Bessel differential equation.

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

Terminating Laguerre polynomials.

(35)

(36)

(37)

(38)

(39)

(40)

(41)

(42)

Terminating Legendre polynomials.

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

Chebyshev differential equation.

(51)

(52)

(53)

(54)

Compatibility

• 

The RandomTools[GenerateSimilarODE] command was introduced in Maple 2021.

• 

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

See Also

HowDoI,WorkWithRandomGenerators

InertForm

rand

RandomTools

RandomTools[Generate]

RandomTools[GenerateSimilar]

randpoly

 


Download Help Document