The order of the differential equation (d^3y/dx^3)^4 + d^4y/dx^4 + (dy/dx) = 0 is Option 1: 4 Option 2: 3 Option 3: 1 Option 4: Not defined

Answer: 4. Solution: Order is the highest order derivative present, irrespective of powers or of the term. Here d^4y/dx^4 is the highest, so the order is 4. (The (dy/dx) term only makes the degree undefined, not the order.)

Calculus

Differential Equations

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The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is

Not defined

✅ Correct Option: 1

Order is the highest order derivative present, irrespective of powers or of the $\log$ term. Here $\frac{d^4y}{dx^4}$ is the highest, so the order is 4. (The $\log\left(\frac{dy}{dx}\right)$ term only makes the degree undefined, not the order.)

2023: 15 June Shift 2

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :

2023: 15 June Shift 2

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(D) second order

Choose the correct answer from the options given below :

2025: 22 May Shift 1

Which of the following statements is/are true?

(A) $(\tan^{-1} y - x)dy = (1 + y^2)dx$ is a differential equation where variables are separable.

(B) $(1 + x^2)dy + 2xydy = \cot x \ dx (x \neq 0)$ is a first order linear differential equation.

(D) $(xy)dx - (x + y^2)dy = 0$ is a homogeneous differential equation.

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
Differential equation	Degree
(A) $\frac{d^2y}{dx^2} + \sqrt{\frac{dy}{dx}} - y = 0$	(I) 6
(B) $\sqrt{\frac{d^3y}{dx^3}} - \sqrt[12]{\frac{d^2y}{dx^2}} = 0$	(II) Not defined
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} + e^{\frac{dx}{dx}} = x^2$	(III) 3
(D) $\sqrt[3]{\frac{dy}{dx}} - \frac{d^2y}{dx^2} = e^x$	(IV) 2

Choose the correct answer from the options given below:

2026: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $y + \frac{dy}{dx} = \frac{1}{4}\int y\,dx$	(I) Order 1, Degree 1
(B) $y = \frac{dy}{dx} + \frac{C}{dy/dx}$	(II) Order 2, Degree 2
(C) $(xy^2+x)dx + (y-x^2)dy = 0$	(III) Order 2, Degree 1
(D) $\left[\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2}/\frac{d^2y}{dx^2}\right] = K$	(IV) Order 1, Degree 2

Choose the correct answer from the options given below:

2025: 30 May Shift 2

The general solution of the differential equation $x\left(\frac{dy}{dx}\right) = y + x \tan\left(\frac{y}{x}\right)$ is

The order of the differential equation (d3ydx3)4+d4ydx4+log⁡(dydx)=0\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0(dx3d3y​)4+dx4d4y​+log(dxdy​)=0 is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is