Question

Solve: √(x + y + 1).(dy/dx) = x + y – 1. 

Answer 1

The given differential equation is

dy/dx = (x + y – 1)/√(x + y + 1)  ...(i)

Let x + y + 1 = v²

1 + (dy/dx) = 2v(dv/dx)

dy/dx = 2v(dv/dx) – 1

 2v(dv/dx) –1 = (v² – 2)/v

which is the required solution.