If m and n are order and degree of the differential equation `((d^2y)/(dx^2))^5+(4((d^2y)/(dx^2))^3)/((d^3y)/(dx^3))+(d^3y)/(dx^3)=x^2-1` (A) `m=3, n=1` (B) `m=3, n=3` (C) `m=3, n=2` (D) `m=3, n=5`

Options

A. `m=3, n=3`
B. `m=3, n=2`
C. `m=3, n=5`
D. `m=3, n=1`

Answer

D

Explanation

The given differential equation can be rewritten as
`((d^(2)y)/(dx^(2)))^(5)*(d^(3)y)/(dx^(3))+4((d^(2)y)/(dx^(2)))^(3)+((d^(3)y)/(dx^(3)))^(2)`
`=(x^(2)-1)(d^(3)y)/(dx^(3))implies`order(m)=3
and degree `(n)=2`