Consider the differential equation dy/dx + y x = x, then which of the following statements are correct? (A) It is homogeneous (B) It has x as its integrating factor (C) It's general solution is y x = x + c, where c is arbitary constant. (D) It's degree is not defined Choose the correct answer from the options given below: Option 1: (A) and (D) only Option 2: (B) and (C) only Option 3: (C) and (D) only Option 4: (B), (C) and (D) only

The answer is '(B) and (C) only'. View full solution:

Calculus > Differential Equations

Medium

core

Consider the differential equation $\frac{dy}{dx} + y \tan x = \sec x$, then which of the following statements are correct? (A) It is homogeneous (B) It has $\sec x$ as its integrating factor (C) It's general solution is $y \sec x = \tan x + c$, where c is arbitary constant. (D) It's degree is not defined Choose the correct answer from the options given below:

(A) and (D) only

(B) and (C) only

(B), (C) and (D) only

✅ Correct Option: 2

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(C) $3+\frac{dy}{dx} = y+\frac{d^3y}{dx^3}$	(III) 4
(D) $\frac{dy}{dx} = x+3$	(IV) 5

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D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$		IV. 3

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B. Degree of a differential equation is a real number.

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