If y= (3 ⁻¹ x ) , then (1-3 x^2 ) d^2 y d x^2 -12 x d y d x =

Step-by-step solution

y= (3 ⁻¹ x ) Let ⁻¹ x= =x y= 3 = 3 - ^3 1-3 ^2 = 3 x-x^3 1-3 x^2 (1-3 x^2 ) y=3 x-x^3 On differentiating both sides w.r.t. x , (1-3 x^2 ) d y d x +y(-6 x)=3-3 x^2 Again, differentiating both sides w.r.t. x , (1-3 x^2 ) d^2 y d x^2 +(-6 x) d y d x -6 (x d y d x +y )=-6 x (1-3 x^2 ) d^2 y d x^2 -12 x d y d x =6(y-x)