Exact Differential Equation - Practice Questions & MCQ

Sometimes some differential equations can be solved using observation only. In such equations we can get differential of a function of x and y both.

Illustration 1 :

Let us first separate terms containing only x with dx and terms containing only y with dy

Here first two terms have both x and y. We can make an observation that first two terms are the differentiation of x²y. Hence we can write this equation as

Integrating this, we get

This is the solution of this equation

The presence of following exact differentials should be observed in a given differential equation

Illustration 2 :

Observe that

So the equation is

Integrating