Question

Solve the differential equation (dy/dx) + (y/x) = y²/x².

Answer 1

(dy/dx) + (y/x) = y²/x² ...(i)

equation (i) is a homogenous differential equation. To solve it we make substitution y = Vx differentiating y = Vx with respective to x

Integrating both sides

 

Putting the value of A & B in equation (iii)

1/V(V - 2) = -(1/V) + (1/2(V - 2)

from equation (ii)