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Student[ODEs]

  

IntegratingFactor

  

find an integrating factor for an ODE

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IntegratingFactor(ODE, y(x))

Parameters

ODE

-

an ordinary differential equation

y

-

name; the dependent variable

x

-

name; the independent variable

Description

• 

IntegratingFactor(ODE, y(x)) attempts to find an integrating factor for an ODE.

• 

Multiplying by the integrating factor makes the ODE exact, that is, a total derivative with respect to x. The new equation can then be solved by simply integrating with respect to x.

Examples

withStudentODEs:

ode1diffzt,tt1zt2=t2zt+1

ode1ⅆⅆtztt1zt2=t2zt+1

(1)

μ1IntegratingFactorode1,zt

μ11zt+1t1

(2)

exact_ode1μ1ode1

exact_ode1ⅆⅆtztzt2zt+1=t2t1

(3)

Integrateexact_ode1,zt

zt22zt+lnzt+1=t22tlnt1+_C1

(4)

ode2diffyx,x,x,x=xdiffyx,x+yxdiffyx,x,xyxx

ode2ⅆ3ⅆx3yx=xⅆⅆxyx+yxⅆ2ⅆx2yxyxx

(5)

μ2IntegratingFactorode2,yx

μ21yxx

(6)

exact_ode2μ2ode2

exact_ode2ⅆ3ⅆx3yxyxx=xⅆⅆxyx+yxⅆ2ⅆx2yxyx2x2

(7)

solIntegrate:-Applyexact_ode2,yx

solxⅆⅆxyx+yxⅆ2ⅆx2yxyx2x2ⅆ3ⅆx3yxyxxⅆx=0ⅆx+_C1

(8)

Integrate:-Evaluatesol

ⅆ2ⅆx2yxyxx=_C1

(9)

Compatibility

• 

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

• 

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

See Also

DEtools[intfactor]

dsolve

Student

Student[ODEs]

Student[ODEs][Integrate]