If ⁻¹ ( x^2-y^2 x^2+y^2 )= a , then d^2 y d x^2 equals

Step-by-step solution

We have ⁻¹ ( x^2-y^2 x^2+y^2 )= a x^2-y^2 x^2+y^2 = ( a) 1- ^2 1+ ^2 = ( a) (on putting y=x .) aligned & & 2 & = ( a) & & 2 & = ⁻¹( a) & & & = 1 2 ⁻¹ ( a) aligned ⁻¹ ( y x )= 1 2 ⁻¹ a 1 1+ y^2 x^2 x d y d x -y x^2 =0 x d y d x -y=0 d y d x = y x ....(i) d^2 y d x^2 = -y x^2 + 1 x d y d x = -y x^2 + 1 x ( y x ) ; from (i) d^2 y d x^2 = -y x^2 + y x^2 =0 .