Question

If y = t(x) be a differentiable function ᵾ x € R, then which of the following is always true?

(a) d^2y/dx^2 – (dy/dx)^3 = 0

(b) d^2y/dx^2 + (dy/dx)^3 d^2x/dy^2 = 0

(c) d^2y/dx^2 – (dx/dy)^3 = 0

(d) d^2y/dx^2 + (dy/dx)^3 = 0

I had been asked this question during a job interview.

My question is from Linear Second Order Differential Equations topic in portion Differential Equations of Mathematics – Class 12

Answer 1

Correct option is (b) d^2y/dx^2 + (dy/dx)^3 d^2x/dy^2 = 0

For explanation I would say: (dy/dx)= (dx/dy)^-1

So, d^2y/dx^2 = – (dx/dy)^-2 d/dx(dx/dy)

= – (dy/dx)^2(d^2x/dy^2)(dy/dx)

=> d^2y/dx^2 + (dy/dx)^3 d^2x/dy^2 = 0