Category:Integrating Factors
This category contains results about Integrating Factors.
Definitions specific to this category can be found in Definitions/Integrating Factors.
Consider the first order ordinary differential equation:
- $(1): \quad \map M {x, y} + \map N {x, y} \dfrac {\d y} {\d x} = 0$
such that $M$ and $N$ are real functions of two variables which are not homogeneous functions of the same degree.
Suppose also that:
- $\dfrac {\partial M} {\partial y} \ne \dfrac {\partial N} {\partial x}$
Then from Solution to Exact Differential Equation, $(1)$ is not exact, and that method can not be used to solve it.
However, suppose we can find a real function of two variables $\map \mu {x, y}$ such that:
- $\map \mu {x, y} \paren {\map M {x, y} + \map N {x, y} \dfrac {\d y} {\d x} } = 0$
is exact.
Then the solution of $(1)$ can be found by the technique defined in Solution to Exact Differential Equation.
The function $\map \mu {x, y}$ is called an integrating factor.
Pages in category "Integrating Factors"
The following 12 pages are in this category, out of 12 total.
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- Integrating Factor for First Order ODE
- Integrating Factor for First Order ODE/Conclusion
- Integrating Factor for First Order ODE/Examples
- Integrating Factor for First Order ODE/Function of One Variable
- Integrating Factor for First Order ODE/Function of Product of Variables
- Integrating Factor for First Order ODE/Function of Sum of Variables
- Integrating Factor for First Order ODE/Preliminary Work
- Integrating Factor for First Order ODE/Technique for finding Integrating Factor