Class 12 Maths, Worked in Full Past papersGet updates
CBSE Board Examination 2023 · Section A · 1 mark

Q7: Order plus degree of d2ydx2+(dydx)3=sin⁡y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 = \sin y

Board 2023Ch 9 · Differential Equations
The question

The sum of the order and the degree of the differential equation d2ydx2+(dydx)3=sin⁡y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 = \sin y is :

(a) 55

(b) 22

(c) 33

(d) 44

Exam answer

The derivatives in the equation are dydx\frac{dy}{dx} and d2ydx2\frac{d^2y}{dx^2}⁠.

The highest order derivative is d2ydx2\frac{d^2y}{dx^2}⁠, so the order is 2.

Why?

The order of a differential equation is the order of the highest derivative in it. A second derivative beats a first derivative, so the order is 2.

The equation is a polynomial in the derivatives and the power of d2ydx2\frac{d^2y}{dx^2} is 1, so the degree is 1.

Why?

The degree is the power of the highest order derivative, once the equation is a polynomial in its derivatives. Here d2ydx2\frac{d^2y}{dx^2} appears to the power 1.

Watch out: the cube belongs to dydx\frac{dy}{dx}⁠, which is not the highest derivative, so it does not set the degree. And sin⁡y\sin y is a function of yy only, not of a derivative, so the degree is still defined.

Sum =2+1=3= 2 + 1 = 3⁠.

Answer: (c) 33

Where this comes from

Chapter 9, Differential Equations: Order and degree of a differential equation.

Question type: Order and degree

How to spot it: click to see

Type 1. Order and degree: the highest derivative, and its power

Spot it: "find the order and degree (if defined)". Often an MCQ.

Here: The highest derivative is d2ydx2\frac{d^2y}{dx^2}⁠, so the order is 2. The sin⁡\sin is on yy⁠, not on a derivative, so the degree is still defined: it is 1, and the sum is 3.

Quick lesson · Worked NCERT solutions · Interactive lesson

Found an error?

Tell us if something on this page is wrong or unclear. Send feedback on this question →

Differential Equations in past papers: question 9 of 31 · see them all