Which of the following are linear first order differential equations? (A) $\frac{dy}{dx} + P(x)y = Q(x)$ (B) $\frac{dx}{dy} + P(y)x = Q(y)$ (C) $(x - y)\frac{dy}{dx} = x + 2y$ (D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$ Choose the correct answer from the options given below:
(A), (B) and (D) only
(A) and (B) only
(A), (B) and (C) only
(A), (B), (C) and (D)

Question

Which of the following are linear first order differential equations? (A) $\frac{dy}{dx} + P(x)y = Q(x)$ (B) $\frac{dx}{dy} + P(y)x = Q(y)$ (C) $(x - y)\frac{dy}{dx} = x + 2y$ (D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$ Choose the correct answer from the options given below:

(A), (B) and (D) only

(A) and (B) only

(A), (B) and (C) only

(A), (B), (C) and (D)

Option 1: (A), (B) and (D) only

Option 2: (A) and (B) only

Option 3: (A), (B) and (C) only

Option 4: (A), (B), (C) and (D)

AfterBoards · Accepted Answer

The answer is '(A), (B) and (D) only'. View full solution:

	LIST-I Differential equation		LIST-II Integrating factor
A.	$\dfrac{dy}{dx} + 3y = e^{-2x}$	I.	$\dfrac{1}{x}$
B.	$x\dfrac{dy}{dx} + y = 3x^2$	II.	$e^{-x}$
C.	$x\dfrac{dy}{dx} - y = 3x^2$	III.	$x$
D.	$\dfrac{dy}{dx} - y = x$	IV.	$e^{3x}$