The solution of differential equation y(1 - x^2)dy/dx = x(1 + y^2) is : Option 1: (1 + y^2), 1 - x^2, = C Option 2: (1 + y^3), 1 - x^2, = C Option 3: (1 + y^4), 1 - x^2, = C Option 4: √(1 + y^2), 1 - x^2, = C

Answer: (1 + y^2), 1 - x^2, = C. Solution: Separate: (y dy)/(1+y^2) = (x dx)/(1-x^2). Integrate: 1/2(1+y^2) = -1/2, 1-x^2, + C_1. So [(1+y^2), 1-x^2, ] = 2C_1, giving (1+y^2), 1-x^2, = C.

Calculus

Differential Equations

Medium

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :

$(1 + y^2)|1 - x^2| = C$

$(1 + y^3)|1 - x^2| = C$

$(1 + y^4)|1 - x^2| = C$

$\sqrt{1 + y^2}|1 - x^2| = C$

✅ Correct Option: 1

Separate: $\frac{y\,dy}{1+y^2} = \frac{x\,dx}{1-x^2}$ . Integrate: $\frac{1}{2}\log(1+y^2) = -\frac{1}{2}\log|1-x^2| + C_1$ . So $\log[(1+y^2)|1-x^2|] = 2C_1$ , giving $(1+y^2)|1-x^2| = C$ .

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
Differential equation	Order and degree
(A) $y''' + x^2(y'')^3 + y = 0$	(I) $3, 2$
(B) $y''' + y^2 + e^{y'} = 0$	(II) $3, 3$
(C) $(y''')^2 + x^2(y'')^3 + xy = 0$	(III) $3, 1$
(D) $(y''')^3 + x(y'')^2 + y = 0$	(IV) $3, \text{Not defined}$

Choose the correct answer from the options given below:

2025: 15 May Shift 2

Consider the curve which is represented by the differential equation $\frac{dy}{dx} = 1 + x + y + xy$ . If it passes through the point $(0,0)$ , then which of the following is/are true?

(A) it is a straight line.

(B) it is a parabola.

(D) Its equation is $xy(x + 1)\left(y - \frac{1}{\sqrt{e}} + 1\right) = 0$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Solution of differential equation $\frac{dy}{dx} = e^{x+y} - xe^y$ is

2023: 23 May Shift 3

The general solution of $\frac{dy}{dx} = 1 + x^2 + y^2 + x^2y^2$ is:

(given that $C$ is the constant of integration)

2025: 13 May Shift 1

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

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^{1/4} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^4 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

Choose the correct answer from the options given below:

The solution of differential equation y(1−x2)dydx=x(1+y2)y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)y(1−x2)dxdy​=x(1+y2) is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :