The slope of tangent at (x, y) to a curve passing through (1, 4 ) is y x - ^2 y x , then the equation of curve is

Step-by-step solution

d y ~d x = y x - ^2 y x ...(i) Put y=v x ...(ii) d y ~d x = v +x dv ~d x ...(iii) Substituting (ii) and (iii) in (i), we get. v +x ~d v ~d x = v - ^2 v x dv ~d x =- ^2 v Integrating on both sides, we get aligned & ^2 v d v=- d x x +c & v=- x+c & y x =- x+c...(iv) aligned Since the required curve passes through (1, 4 ) , aligned & 4 =- 1+ c c =1 & y x =- x+1 & y x =- x+ e & y=x ⁻¹ [ ( e x ) ] aligned ...[From (iv)]