## Problem 04 | Determination of Integrating Factor

Problem 04
$y(4x + y)~dx - 2(x^2 - y)~dy = 0$

## Problem 03 | Determination of Integrating Factor

Problem 03
$y(2x - y + 1)~dx + x(3x - 4y + 3)~dy = 0$

## Integrating Factors Found by Inspection

The following are the four exact differentials that occurs frequently.

1. $d(xy) = x \, dy + y \, dx$

2. $d\left( \dfrac{x}{y} \right) = \dfrac{y \, dx - x \, dy}{y^2}$

3. $d\left( \dfrac{y}{x} \right) = \dfrac{x \, dy - y \, dx}{x^2}$

4. $d\left( \arctan \dfrac{y}{x} \right) = \dfrac{x \, dy - y \, dx}{x^2 + y^2}$
5.

6. $d\left( \arctan \dfrac{x}{y} \right) = \dfrac{y \, dx - x \, dy}{x^2 + y^2}$