The degree of the differential equation
`((d^(3)y)/(dx^(3)))^(2//3)+4-3(d^(2)y)/(dx^(2))+5(dy)/(dx)=0,` is

Options

A. 3
B. 2
C. `2//3`
D. Not defined

Answer

B

Explanation

Degree of a differential equation is the power to which the highest derivative is raised when it is expressed as polynomial of derivatives.
Given equation is
` ((d^(3)y)/(dx^(3)))^(2//3) -3 ((d^(2)y)/(dx^(2))) -5 ((dy)/(dx)) +4 =0`
` Rightarrow ((d^(3)y)/(dx^(3)))^(2//3) = 3 (d^(2)y)/(dx^(2)) -5 (dy)/(dx) =4`
Cube on both side,
`((d^(3)y)/(dx^(3)))^(2) = [ 3 (d^(2)y)/(dx^(2)) -5 (dy)/(dx)-4] ^(3)`
Hence, degree = 2