Category:Definitions/Integrating Factors
This category contains definitions related to Integrating Factors.
Related results can be found in Category: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 "Definitions/Integrating Factors"
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