Student[ODEs]
IntegratingFactor
find an integrating factor for an ODE
Calling Sequence
Parameters
Description
Examples
Compatibility
IntegratingFactor(ODE, y(x))
ODE
-
an ordinary differential equation
y
name; the dependent variable
x
name; the independent variable
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.
withStudentODEs:
ode1≔diffzt,tt−1zt2=−t2zt+1
ode1≔ⅆⅆtztt−1zt2=−t2zt+1
μ1≔IntegratingFactorode1,zt
μ1≔1zt+1t−1
exact_ode1≔μ1ode1
exact_ode1≔ⅆⅆtztzt2zt+1=−t2t−1
Integrateexact_ode1,zt
zt22−zt+lnzt+1=−t22−t−lnt−1+_C1
ode2≔diffyx,x,x,x=xdiffyx,x+yxdiffyx,x,xyxx
ode2≔ⅆ3ⅆx3yx=xⅆⅆxyx+yxⅆ2ⅆx2yxyxx
μ2≔IntegratingFactorode2,yx
μ2≔1yxx
exact_ode2≔μ2ode2
exact_ode2≔ⅆ3ⅆx3yxyxx=xⅆⅆxyx+yxⅆ2ⅆx2yxyx2x2
sol≔Integrate:-Applyexact_ode2,yx
sol≔∫xⅆⅆxyx+yxⅆ2ⅆx2yxyx2x2−ⅆ3ⅆx3yxyxxⅆx=∫0ⅆx+c__1
Integrate:-Evaluatesol
−ⅆ2ⅆx2yxyxx=c__1
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][Integrate]
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