If p and q are order and degree of differential equation `y^(2)((d^(2)y)/(dx^(2)))^(2)+3x((dy)/(dx))^(1/3) + x^(2)y^(2) = sin x, then`

Options

A. `p gt q`
B. `(p)/(q) = (1)/(2)`
C. `p = q`
D. `p lt q`

Answer

D

Explanation

`y^(2)((d^(2)y)/(dx^(2)))^(2)+x^(2)y^(2)- sin x = - 3x((dy)/(dx))^(1/3)`
`therefore" "(y^(2)((d^(2)y)/(dx^(2)))^(2)+x^(2)y^(2)- sin x)^(3) = - 27x^(3)((dy)/(dx))`
Here order = 2 = p
Degree = 6 = q
`therefore" "p lt q`