Write order and degree (if defined)of differential equations: √(1-(dy/dx)^2)=(a(d^2y/dx^2))^(1/3)

Question

Write order and degree (if defined)of differential equations: 

\(\sqrt{1-\left(\cfrac{dy}{dx}\right)^2}=\left(a\cfrac{d^2y}{dx^2}\right)^{1/3}\)

√(1-(dy/dx)²)=(a(d²y/dx²))^1/3

Answer 1

The order of a differential equation is the order of the highest derivative involved in the equation. So the

order comes out to be 2/3 as we have \(\sqrt{1-\left(\cfrac{dy}{dx}\right)^2}=\left(a\cfrac{d^2y}{dx^2}\right)^{1/3}\)

and the degree is the highest power to which a derivative is raised. So the power at this order is 2.

So the answer is 2/3, 2.