If x+y= ⁻¹ y and d² y d x² =f(y) d y d x , then f(y) is equal to

Step-by-step solution

Given, x+y= ⁻¹ y On differentiating w.r.t. x , we get array ll & 1+ d y d x = 1 1+y² d y d x & (1- 1 1+y² ) d y d x =-1 & y² 1+y² d y d x =-1 & d y d x =- ( 1+y² y² )=-1- 1 y² array Again, differentiating w.r.t. x , we get aligned d² y d x² &=0+ 2 y³ d y d x d² y d x² &= 2 y³ d y d x but given, d² y d x² &=f(y) d y d x aligned On comparing, we get f(y)= 2 y³