If ⁻¹ ( y b )=2 ( x 2 ) , where x>0 , then x^2 d^2 y d x^2 +x d y d x is equal to

Step-by-step solution

⁻¹ ( y b )=2 ( x 2 ), x>0 On differentiating w.r.t. x we get array cc & - 1 1- y^2 b^2 1 b d y d x =2 1 ( x 2 ) 1 2 & - 1 b^2-y^2 d y d x = 2 x & x d y d x =-2 b^2-y^2 array Again, differentiating w.r.t. x we get, aligned & x d^2 y d x^2 + d y d x =-2 1 2 (b^2-y^2 )^ -1 / 2 (-2 y) d y d x & x d^2 y d x^2 + d y d x = 2 y b^2-y^2 d y d x & x d^2 y d x^2 + d y d x = 2 y - x 2 d y d x d y d x [from Eq. (i)] & x^2 d^2 y d x^2 +x d y d x =-4 y aligned