Question

Find the curve passing through (2, 0) and having slope of tangent at any point P(x, y) as (((x + 1)² + (y – 3))/(x + 1)). Find also the area enclosed by the curve and x-axis in the fourth quadrant.

Answer 1

Given 

which is a linear differential equation.

Thus, 

Therefore, the solution is

Put x = 2 and y = 0, then c = –3

Hence, the equation of the curve is

y/(x + 1) = x + (3/(x + 1)) – 3 

y = x² + x + 3 – 3x – 3 = x² – 2x

Hence, the required area