The solution of the differential equation dy/dx = /x is Option 1: √x + √y = C; C is an arbitrary constant Option 2: √x - √y = C; C is an arbitrary constant Option 3: √(y/x) + C = 0; C is arbitrary constant Option 4: √(x/y) + C = 0; C is an arbitrary constant

Answer: √x - √y = C; C is an arbitrary constant. Solution: Solution Coming Soon

Calculus

Differential Equations

Easy

common

The solution of the differential equation $\frac{dy}{dx} = \sqrt\frac{{y}}{x}$ is

$\sqrt{x} + \sqrt{y} = C$ ; C is an arbitrary constant

$\sqrt{x} - \sqrt{y} = C$ ; C is an arbitrary constant

$\sqrt{\frac{y}{x}} + C = 0$ ; C is arbitrary constant

$\sqrt{\frac{x}{y}} + C = 0$ ; C is an arbitrary constant

✅ Correct Option: 2

Solution Coming Soon

2022: 4 Aug Shift 1

The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is

2025: 22 May Shift 1

The solution of the differential equation $\frac{dy}{dx} - \frac{y}{x} = 2\log_e x$

2025: 15 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2026: 18 May Shift 1

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$ ; $x \neq 0$ with $y = 1$ when $x = 1$ , is

2023: 15 June Shift 2

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :

2026: 21 May Shift 2

Match the LIST-I with LIST-II

LIST-I (Differential Equation)		LIST-II (Degree of Differential Equation)
A. $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 - \dfrac{dy}{dx} + y = 0$		I. 2
B. $\dfrac{dy}{dx} + \left(\dfrac{d^2y}{dx^2}\right)^4 + 2\left(\dfrac{d^3y}{dx^3}\right)^3 = 0$		II. 4
C. $\left(\dfrac{d^3y}{dx^3}\right)^2 + \left(\dfrac{d^2y}{dx^2}\right)^4 - y = 0$		III. 1
D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$		IV. 3

Choose the correct answer from the options given below: