Order and degree of the differential equation ydy/dx + 4/(dy/dx) = 5 are Option 1: 1, 2 respectively Option 2: 1, 1 respectively Option 3: 1, 0 respectively Option 4: 2, 1 respectively

Answer: 1, 2 respectively. Solution: ydy/dx + 4/(dy/dx) = 5. Multiply by dy/dx: y(dy/dx)^2 + 4 = 5dy/dx. Highest-order derivative is dy/dx (order 1), and the highest power after rationalisation is 2. Hence order = 1, degree = 2.

Calculus

Differential Equations

Easy

Order and degree of the differential equation $y\frac{dy}{dx} + \frac{4}{\frac{dy}{dx}} = 5$ are

1, 2 respectively

1, 1 respectively

1, 0 respectively

2, 1 respectively

✅ Correct Option: 1

$y\frac{dy}{dx} + \frac{4}{dy/dx} = 5$ .

Multiply by $\frac{dy}{dx}$ : $y\left(\frac{dy}{dx}\right)^2 + 4 = 5\frac{dy}{dx}$ .

Highest-order derivative is $\frac{dy}{dx}$ (order 1), and the highest power after rationalisation is 2. Hence order = 1, degree = 2.

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Sum of the order and the degree of the differential equation
A.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$	I.	$2$
B.	$4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$	II.	$3$
C.	$x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$	III.	$5$
D.	$\dfrac{dy}{dx} = x^4 e^{-3y}$	IV.	$4$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

The degree of the differential equation

$\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

2022: 7 Aug Shift 2

If $U(x) = x + \sqrt{1 + x^2}$ , then solution of the differential equation $\frac{dy}{dx} + \sqrt{\frac{1 + y^2}{1 + x^2}} = 0$ , is :

2026: 18 May Shift 2

The integrating factor of the differential equation $y\log_e(10y).\dfrac{dx}{dy}+x=\dfrac{1}{[\log_e(10y)]^2}$ , is

2026: 22 May Shift 1

The general solution of the differential equation $\frac{dy}{dx}=e^{2x-y}+xe^{-y}$ is:

2026: 18 May Shift 2

Match the LIST-I with LIST-II

LIST-I Differential equation	LIST-II Order and degree
A. $y'' = [1+(y')^2]^{3/2}$	I. 3, 4
B. $y''' + y' + y = 2x$	II. 2, 2
C. $2(y'')^3 - (y')^4 + y = 0$	III. 3, 1
D. $(y''')^4 + (y'')^3 + y' + y = 0$	IV. 2, 3

Choose the correct answer from the options given below:

Order and degree of the differential equation ydydx+4dydx=5y\frac{dy}{dx} + \frac{4}{\frac{dy}{dx}} = 5ydxdy​+dxdy​4​=5 are

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CUET Mathematics Past Year Questions (Topic-Wise)

Order and degree of the differential equation $y\frac{dy}{dx} + \frac{4}{\frac{dy}{dx}} = 5$ are