The general solution of dy/dx = 1 + x^2 + y^2 + x^2y^2 is: (given that C is the constant of integration) Option 1: ^-1 x = y + y^3/3 + C Option 2: ^-1 y = x + x^3/3 + C Option 3: ^-1 x = ^-1 y + C Option 4: ^-1 x + ^-1 y = C

The answer is '^-1 y = x + x^3/3 + C'. View full solution:

CUET Mathematics - The general solution of dy/dx = 1 + x^2 + y^2 + x^2y^2 is: (given that C is the constant of integration) | PYQs + Solutions

CUET Mathematics 2023 23 May Shift 3

Calculus

Easy

$\tan^{-1} x = y + \frac{y^3}{3} + C$

$\tan^{-1} y = x + \frac{x^3}{3} + C$

$\tan^{-1} x = \tan^{-1} y + C$

$\tan^{-1} x + \tan^{-1} y = C$

✅ Correct Option: 2

Related questions:

13 May Shift 1

The general solution of the differential equation $ydx - (x + 2y^2)dy = 0$

14 May Shift 2

Match List-I with List-II

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

Choose the correct answer from the options given below:

21 May Shift 1

The number of arbitrary constants in the general solution of a differential equation with degree 1 and order 3, is