The differential equation satisfied by the family of curve y=a x ( 1 x +b ) , where a, b are parameters, is

Step-by-step solution

Given that, y=a x ( 1 x +b ) On differentiating w.r.t. x , we get aligned y₁ & =a [ ( 1 x +b )-x ( 1 x +b ) (- 1 x^2 ) ] y₁ & =a [ ( 1 x +b )+ 1 x ( 1 x +b ) ] aligned Again differentiating, we get aligned & y₂=a [- ( 1 x +b ) (- 1 x^2 )- 1 x^2 ( 1 x +b ) . & .- 1 x^3 ( 1 x +b ) ] & y₂=- a x x^4 ( 1 x +b ) & x^4 y₂+y=0 aligned