Solution of the differential equation dy/dx = sqrt(1 + x^2 + y^2 + x^2y^2) is : (Here C is an arbitrary constant) Option 1: | y + sqrt(1 + y^2)x + sqrt(1 + x^2) | = C Option 2: | y + sqrt(1 + y^2)x + sqrt(1 + x^2) | = C Option 3: | y + sqrt(1 + y^2)x + sqrt(1 + x^2) | = x/2sqrt(1 + x^2) + C Option 4: | y + sqrt(1 + y^2)x + sqrt(1 + x^2) | = x/2sqrt(1 + x^2) + C

The answer is '| y + sqrt(1 + y^2)x + sqrt(1 + x^2) | = x/2sqrt(1 + x^2) + C'. View full solution:

CUET Mathematics - Solution of the differential equation dy/dx = sqrt(1 + x^2 + y^2 + x^2y^2) is : (Here C is an arbitrary constant) | PYQs + Solutions

CUET Mathematics 2025 19 May Shift 1

Calculus

Hard

core

$\log \left| \frac{y + \sqrt{1 + y^2}}{x + \sqrt{1 + x^2}} \right| = C$

$\log \left| \frac{y + \sqrt{1 + y^2}}{\sqrt{x + \sqrt{1 + x^2}}} \right| = C$

$\log \left| \frac{y + \sqrt{1 + y^2}}{\sqrt{x + \sqrt{1 + x^2}}} \right| = \frac{x}{2}\sqrt{1 + x^2} + C$

$\log \left| \frac{y + \sqrt{1 + y^2}}{x + \sqrt{1 + x^2}} \right| = \frac{x}{2}\sqrt{1 + x^2} + C$

✅ Correct Option: 3

Related questions:

CUET Mathematics 15 May Shift 1

Match List-I with List-II

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

Choose the correct answer from the options given below:

CUET Mathematics 15 May Shift 1

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

CUET Mathematics 13 May Shift 1

Match List-I with List-II

Choose the correct answer from the options given below: