Question

The degree of the differential equation $\biggr\lgroup \frac{d^2y}{dx^2} \biggr\rgroup ^3 + \biggr\lgroup \frac{dy}{dx}\biggr\rgroup ^2 + \sin \biggr\lgroup\frac{dy}{dx}\biggr\rgroup +1 =0$ is
(A) 3
(B) 2
(C) 1
(D) not defined

Answer 1

Answer: option D is correct.

Order=4

Degree=not defined

Solution:

Order of differential equation: Order is the highest numbered derivative in the equation.

Degree of differential equation: Degree is the highest power to which highest numbered derivative is raised when equation is free from radicals.

$\biggr\lgroup \frac{d^2y}{dx^2} \biggr\rgroup ^3 + \biggr\lgroup \frac{dy}{dx}\biggr\rgroup ^2 + \sin \biggr\lgroup\frac{dy}{dx}\biggr\rgroup +1 =0$

here highest numbered derivative is 2

So, order is 2.

That highest number derivative raised to power 3,but first order derivative is also with trigonometric function sin,in such case degree is not defined.

Hope it helps you.