Calculus

Differential Equations

Easy

applied

The order and degree of the differential equation $\left[2+\left(\dfrac{dy}{dx}\right)\right]^{5/2}=7\dfrac{d^3y}{dx^3}$ is

Order = 1, degree = 5

Order = 5, degree = 1

Order = 3, degree = 2

Order = 2, degree = 3

✅ Correct Option: 3

The highest derivative present is $\dfrac{d^3y}{dx^3}$ , so the order is 3.

Squaring both sides to clear the fractional power gives $\left[2+\dfrac{dy}{dx}\right]^5 = 49\left(\dfrac{d^3y}{dx^3}\right)^2$ .

The power of the highest derivative is 2, so the degree is 2.

2025: 16 May Shift 1

The general solution of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$

2026: 18 May Shift 2

The solution of the differential equation $9+y^2\dfrac{dy}{dx}=x^2$ is :

[Where $C$ is an arbitrary constant]

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Differential Equation)		LIST-II (Order and degree)
A.	$\log\left(\dfrac{dy}{dx}\right) + \dfrac{d^2y}{dx^2} = 0$	I.	Order : 3 and degree : not defined
B.	$\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 4$	II.	Order : 2 and degree : 2
C.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dy}{dx} = \sqrt{x}$	III.	Order : 2 and degree : not defined
D.	$\left(1+\left(\dfrac{dy}{dx}\right)^2\right)^{3/2} = \dfrac{d^2y}{dx^2}$	IV.	Order : 2 and degree : 1

Choose the correct answer from the options given below:

2025: 3 June Shift 2

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

2026: 12 May Shift 2

Which of the following differential equations has $y=x$ as one of the particular solution?

2025: 3 June Shift 2

The general solution of the differential equation $\frac{dy}{dx} = -4xy^2$ is given by

The order and degree of the differential equation [2+(dydx)]5/2=7d3ydx3\left[2+\left(\dfrac{dy}{dx}\right)\right]^{5/2}=7\dfrac{d^3y}{dx^3}[2+(dxdy​)]5/2=7dx3d3y​ is