# Category:Exact Differential Equations

Jump to navigation
Jump to search

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.

### E

## Pages in category "Exact Differential Equations"

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