Understanding the Order & Degree of a DE

[Jones1987]

Homework Statement

My question wants me to give the Order of the DE, Degree of the DE, and Non-Linear terms in the DE

Homework Equations

[d^2/dx^2 y(x)]^6 + d^4/dx^4 y(x) + [d^5/dx5 y(x)][d/dx y(x)] + x^4[d^3/dx^3 y(x)] = 3cos(2y(x)) + x^2 - 1

The Attempt at a Solution

I know the Order is 5, I know the Non-Linear are the values in brackets, but my teacher has the answer for the Degree = 1

Why is this? I thought it would be 6, as the degree of a DE is the highest derivative term. Or is it because there are more terms with the power of 1?

 

[LCKurtz]

The degree is the power to which the highest order derivative is raised. Your 5th order derivative is raised to the first power.

 

[Jones1987]

Ahhhhh, I see. Thank you, couldn't find a simple answer for ages. Very much appreciated!