First Order Linear Equation

Category: Differential Equations, Integral Calculus, Algebra

"Published in Newark, California, USA"

Find the general solution for the given equation

Solution:

Consider the given equation

Check if the given equation is exact or not exact as follows

Let 

Let

Since 

The given equation is not an exact equation. In this case, we need to find the integrating factor and then multiply it to the both sides of the equation. Let's consider again the given equation

Arrange the above equation into its standard form as follows

Divide both sides of the equation by dx

Divide both sides of the equation by (x + 1)²

As you notice that the above equation is now already in standard form

where

and

The integrating factor is

Therefore, the general solution for the above equation is