The differential equations of the following type are known as exact differential equations.

**f (x, y) + g (x, y)** $\frac{dy}{dx}$ **= 0**

It is an important condition to be noted that $\frac{d}{dy}$ (f (x, y)) with ‘x’ being constant, $\frac{d}{dx}$ (g (x, y)) with ‘y’ being constant, must be equal along with the formation above for the differential equation to be exact.

**Case 1:**

**a)** Find $\int$f (x, y) dx = M + h (y) OR Find $\int$g (x, y)dy = N + l (x).

**b)** Find $\frac{d}{dy}$ (M + h (y)) and compare it with g (x, y) to find h’ (y).

**c)** Then find h (y) by integrating it.

**d)** Then the solution is given by M + h (y) = C

**Case 2:**

**a)** Find $\int$g (x, y)dy = N + l (x).

**b)** Find $\frac{d}{dx}$ (N + l (x)) and compare it with f (x, y) to find l’ (x).

**c)** Then find l (x) by integrating it.

**d)** Then the solution is given by N + l (x) = C

We could use either of the two cases but which one to use depends upon the fact how easy it is to integrate the given functions. The one that is easier to integrate is been chosen and then the steps are followed accordingly.