Category:Exact Differential Equations

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This category contains results about Exact Differential Equations.


Let a first order ordinary differential equation be expressible in this form:

$\map M {x, y} + \map N {x, y} \dfrac {\d y} {\d x} = 0$

such that $M$ and $N$ are not homogeneous functions of the same degree.


However, suppose there happens to exist a function $\map f {x, y}$ such that:

$\dfrac {\partial f} {\partial x} = M, \dfrac {\partial f} {\partial y} = N$

such that the second partial derivatives of $f$ exist and are continuous.


Then the expression $M \rd x + N \rd y$ is called an exact differential, and the differential equation is called an exact differential equation.

Subcategories

This category has only the following subcategory.

Pages in category "Exact Differential Equations"

The following 2 pages are in this category, out of 2 total.