Match List-I with List-II List-

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Target Exam

CUET

Subject

Section B1

Chapter

Differential Equations

Question:

Match List-I with List-II

List-I	List-II
(A) Integrating factor of $xdy-(y + x^2)dx = 0$	(I) $x^2$
(B) Integrating factor of $xdy + (2y + x^2)dx = 0$	(II) $x^3$
(C) Integrating factor of $(3y-x^2)dx + xdy = 0$	(III) $x$
(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$	(IV) $\frac{1}{x}$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

List-I	List-II
(A) Integrating factor of $xdy-(y + x^2)dx = 0$	(IV) $\frac{1}{x}$
(B) Integrating factor of $xdy + (2y + x^2)dx = 0$	(I) $x^2$
(C) Integrating factor of $(3y-x^2)dx + xdy = 0$	(II) $x^3$
(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$	(III) $x$

(A) x dy − (y + x²) dx = 0
⇒ dy/dx = (y + x²)/x
⇒ dy/dx − (1/x)y = x

Integrating factor (IF) = e^(∫ −1/x dx) = 1/x

⇒ (A) → (IV)

(B) x dy + (2y + x²) dx = 0
⇒ dy/dx = −(2y + x²)/x
⇒ dy/dx + (2/x)y = −x

IF = e^(∫ 2/x dx) = x²
⇒ (B) → (I)

(C) (3y − x²) dx + x dy = 0
⇒ dy/dx = −(3y − x²)/x
⇒ dy/dx + (3/x)y = x

IF = e^(∫ 3/x dx) = x³
⇒ (C) → (II)

(D) (y + 3x²) dx + x dy = 0
⇒ dy/dx = −(y + 3x²)/x
⇒ dy/dx + (1/x)y = −3x

IF = e^(∫ 1/x dx) = x
⇒ (D) → (III)