If y= ( ⁻¹ x )^2+ ( ⁻¹ x )^2 , then (1-x^2 ) y₂-x y₁=

Step-by-step solution

aligned & y= ( ⁻¹ x )^2+ ( ⁻¹ x )^2 & d y ~d x = 2 ⁻¹ x 1-x^2 - 2 ⁻¹ x 1-x^2 & d y ~d x = 2 ( ⁻¹ x- ⁻¹ x ) 1-x^2 & 1-x^2 d y ~d x =2 ( ⁻¹ x- ⁻¹ x ) aligned Differentiating both sides w.r.t. x , we get aligned & 1-x^2 d ^2 y ~d x^2 + d y ~d x 1 2 1-x^2 (-2 x) & =2 ( 1 1-x^2 - (-1) 1-x^2 )= 4 1-x^2 & (1-x^2 ) d ^2 y ~d x^2 -x d y ~d x =4 aligned