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Student[ODEs][Solve]

  

ByPerturbation

  

Solve a second order ODE by the perturbation method

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ByPerturbation(ODE, y(x))

Parameters

ODE

-

a second order ordinary differential equation by the perturbation method

y

-

name; the dependent variable

x

-

name; the independent variable

Description

• 

The ByPerturbation(ODE, y(x)) command finds the solution of a second order ODE by the perturbation method.

Examples

withStudentODEsSolve:

ode1diffyx,x,x+yxsinεyx=0

ode1ⅆ2ⅆx2yx+yxsinεyx=0

(1)

ic1evaldiffyx,x,x=0=1,y0=0

ic1ⅆⅆxyxx=0|ⅆⅆxyxx=0=1,y0=0

(2)

ByPerturbationode1,ic1,yx,ε,3

yτ=sinτ+ε3sinτ48sinτcosτ248

(3)

ode2diffyx,x,x+4yx+2diffyx,x+εyx+cosεyx=0

ode2ⅆ2ⅆx2yx+4yx+2ⅆⅆxyx+εyx+cosεyx=0

(4)

ic2evaldiffyx,x,x=0=0,y0=14

ic2ⅆⅆxyxx=0|ⅆⅆxyxx=0=0,y0=14

(5)

ByPerturbationode2,ic2,yx,ε,1

yx=14+εⅇxsin3x348ⅇxcos3x16+116

(6)

ode3diffyx,x,x+yx+εyx3=0

ode3ⅆ2ⅆx2yx+yx+εyx3=0

(7)

ic3evaldiffyx,x,x=0=0,y0=1

ic3ⅆⅆxyxx=0|ⅆⅆxyxx=0=0,y0=1

(8)

ByPerturbationode3,ic3,yx,ε,2

yτ=cosτ+εcosτ8+cosτ38+ε225cosτ256+cosτ56429cosτ3256

(9)

ode4diffyx,x,x+εx+1yx=0

ode4ⅆ2ⅆx2yx+εx+1yx=0

(10)

ic4evaldiffyx,x,x=0=0,y0=1

ic4ⅆⅆxyxx=0|ⅆⅆxyxx=0=0,y0=1

(11)

ByPerturbationode4,ic4,yx,ε,2

yx=cosx+εcosxx4+sinxx24sinx4ε2xx37xcosx+sinx10x23+732

(12)

Compatibility

• 

The Student[ODEs][Solve][ByPerturbation] command was introduced in Maple 2021.

• 

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

See Also

dsolve

Student

Student[ODEs]

Student[ODEs][Solve]