If x = at^2 and y = 2at, then show that xy (d^2 y/dx^2) + a = 0

Question

If x = at² and y = 2at, then show that \(xy \frac{d^2 y}{dx^2} + a = 0\)

xy (d²y/dx²) + a = 0

Answer 1

x = at² and y = 2at .....(1)

Differentiating x and y w.r.t. t, we get