The solution of the differential equation dy/dx = x^2+xy+y^2/x^2 for x>0, y>0 at x=1, y=2 is Option 1: (y/x) = _e x + 2 Option 2: ^-1(x/y) = _e x + ^-12 Option 3: ^-1y/x = _e x + ^-12 Option 4: ^-1y/x = _e x - ^-12

The answer is '^-1y/x = _e x + ^-12'. View full solution:

CUET Mathematics - The solution of the differential equation dy/dx = x^2+xy+y^2/x^2 for x>0, y>0 at x=1, y=2 is | PYQs + Solutions

CUET Mathematics 2026 15th May Shift 1

Calculus

Medium

core

$\tan\left(\dfrac{y}{x}\right) = \log_e x + \tan 2$

$\tan^{-1}\left(\dfrac{x}{y}\right) = \log_e x + \tan^{-1}2$

$\tan^{-1}\dfrac{y}{x} = \log_e x + \tan^{-1}2$

$\tan^{-1}\dfrac{y}{x} = \log_e x - \tan^{-1}2$

✅ Correct Option: 3

Related questions:

22nd May Shift 2

Match List-I with List-II

List-I: Linear differential equation	List-II: Integrating factor
(A) $x\frac{dy}{dx}-y=2x^3$	(I) $e^{-x}$
(B) $2x\frac{dy}{dx}+y=3x^2$	(II) $e^x$
(C) $\frac{dy}{dx}+y=\cos x-\sin x$	(III) $x^{1/2}$
(D) $\frac{dy}{dx}-y=e^x$	(IV) $1/x$

Choose the correct answer from the options given below:

15 May Shift 1

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

(D) It's degree is not defined

Choose the correct answer from the options given below:

15 May Shift 1

The general solution of the differential equation $(1 + e^x)dy + ye^x dx = 0$ , where $y > 0$ , is