Student[ODEs][Solve]
ByPerturbation
Solve a second order ODE by the perturbation method
Calling Sequence
Parameters
Description
Examples
Compatibility
ByPerturbation(ODE, y(x))
ODE
-
a second order ordinary differential equation by the perturbation method
y
name; the dependent variable
x
name; the independent variable
The ByPerturbation(ODE, y(x)) command finds the solution of a second order ODE by the perturbation method.
with⁡StudentODEsSolve:
ode1≔diff⁡y⁡x,x,x+y⁡x−sin⁡ε⁢y⁡x=0
ode1≔ⅆ2ⅆx2y⁡x+y⁡x−sin⁡ε⁢y⁡x=0
ic1≔eval⁡diff⁡y⁡x,x,x=0=1,y⁡0=0
ic1≔ⅆⅆxy⁡xx=0|ⅆⅆxy⁡xx=0=1,y⁡0=0
ByPerturbation⁡ode1,ic1,y⁡x,ε,3
y⁡τ=sin⁡τ+ε3⁢sin⁡τ48−sin⁡τ⁢cos⁡τ248
ode2≔diff⁡y⁡x,x,x+4⁢y⁡x+2⁢diff⁡y⁡x,x+ε⁢y⁡x+cos⁡ε⁢y⁡x=0
ode2≔ⅆ2ⅆx2y⁡x+4⁢y⁡x+2⁢ⅆⅆxy⁡x+ε⁢y⁡x+cos⁡ε⁢y⁡x=0
ic2≔eval⁡diff⁡y⁡x,x,x=0=0,y⁡0=−14
ic2≔ⅆⅆxy⁡xx=0|ⅆⅆxy⁡xx=0=0,y⁡0=−14
ByPerturbation⁡ode2,ic2,y⁡x,ε,1
y⁡x=−14+ε⁢−ⅇ−x⁢sin⁡3⁢x⁢348−ⅇ−x⁢cos⁡3⁢x16+116
ode3≔diff⁡y⁡x,x,x+y⁡x+ε⁢y⁡x3=0
ode3≔ⅆ2ⅆx2y⁡x+y⁡x+ε⁢y⁡x3=0
ic3≔eval⁡diff⁡y⁡x,x,x=0=0,y⁡0=1
ic3≔ⅆⅆxy⁡xx=0|ⅆⅆxy⁡xx=0=0,y⁡0=1
ByPerturbation⁡ode3,ic3,y⁡x,ε,2
y⁡τ=cos⁡τ+ε⁢−cos⁡τ8+cos⁡τ38+ε2⁢25⁢cos⁡τ256+cos⁡τ564−29⁢cos⁡τ3256
ode4≔diff⁡y⁡x,x,x+−ε⁢x+1⁢y⁡x=0
ode4≔ⅆ2ⅆx2y⁡x+−ε⁢x+1⁢y⁡x=0
ic4≔eval⁡diff⁡y⁡x,x,x=0=0,y⁡0=1
ic4≔ⅆⅆxy⁡xx=0|ⅆⅆxy⁡xx=0=0,y⁡0=1
ByPerturbation⁡ode4,ic4,y⁡x,ε,2
y⁡x=cos⁡x+ε⁢cos⁡x⁢x4+sin⁡x⁢x24−sin⁡x4−ε2⁢x⁢x3−7⁢x⁢cos⁡x+sin⁡x⁢−10⁢x23+732
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]
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