Write order and degree (if defined)of each of the following differential equations: y=dy/dx+5/(dy/dx)

Question

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

\(y=\cfrac{dy}{dx}+\cfrac{5}{\left(\cfrac{dy}{dx}\right)}\)

y=dy/dx+5/(dy/dx)

Answer 1

Given: \(y=\cfrac{dy}{dx}+\cfrac{5}{\left(\cfrac{dy}{dx}\right)}\)

Solving, we get,

\(y\times\cfrac{dy}{dx}=\left(\cfrac{dy}{dx}\right)^2+5\)

Now,

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 as we have, \(y\times\cfrac{dy}{dx}=\left(\cfrac{dy}{dx}\right)^2+5\)

and the degree is the highest power to which a derivative is raised. So the power at this order is 1. 

So the answer is 2, 1.