Match List-I with List-II List-

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Match List-I with List-II

List-I (Differential equation)	List-II (Order and Degree)
(A) $\frac{d^3y}{dx^3} + y^2+e^{dy/dx} = 0$	(I) order = 3, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}+1=0$	(II) order = 3, degree not defined
(C) $2x^2\frac{d^2y}{dx^2}-3\left(\frac{dy}{dx}\right)^2+y=0$	(III) order = 2, degree = 3
(D) $\frac{d^3y}{dx^3} +2\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}=0$	(IV) order = 2, degree = 1

Choose the correct answer from the options given below:

Options:

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

Correct Answer:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Explanation:

The correct answer is Option (2) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)

List-I (Differential equation)	List-II (Order and Degree)
(A) $\frac{d^3y}{dx^3} + y^2+e^{dy/dx} = 0$	(II) order = 3, degree not defined
(B) $\left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}+1=0$	(III) order = 2, degree = 3
(C) $2x^2\frac{d^2y}{dx^2}-3\left(\frac{dy}{dx}\right)^2+y=0$	(IV) order = 2, degree = 1
(D) $\frac{d^3y}{dx^3} +2\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}=0$	(I) order = 3, degree = 1

Analyze each differential equation for order and degree:

(A) $\frac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$

Contains exponential of derivative ⇒ degree is not defined

Highest order derivative = third order

⇒ (A) → (II)

(B) $\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} + 1 = 0$

Highest order = 2, and highest power = 3

⇒ (B) → (III)

(C) $2x^2 \frac{d^2y}{dx^2} - 3\left( \frac{dy}{dx} \right)^2 + y = 0$

Highest order = 2, and degree = 1 (since no non-integer powers or functions of derivative)

⇒ (C) → (IV)

(D) $\frac{d^3y}{dx^3} + 2\left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} = 0$

Highest order = 3, highest power = 1 (since highest derivative appears linearly)

⇒ (D) → (I)