Question

If nth derivative of xy3 + x^2y2 + x^3y0 = 0 then order of its nth differential equation is,

(a) n

(b) n+1

(c) n+2

(d) n+3

I had been asked this question in a national level competition.

My question is taken from Leibniz Rule topic in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (d) n+3

The explanation: 1. If we differentiate this equation n times then terms comes in nth order differential equation is yn+3, yn+2, yn+1, yn, yn-1, yn-2, yn-3. Hence order of differential equation becomes n+3.

2. By Leibniz rule differentiating it n times, we get

Xyn+3 + nyn+2 + x^2yn+2 + 2nxyn+1 + 2n(n-1)yn + x^3yn + 3nx^2yn-1 + 6n(n-1)xyn-2 + 6n(n-1)(n-2)yn-3 = 0

Hence order of differential equation becomes n+3.