The general solution of the differential equation x(dy/dx) = y + x (y/x) is Option 1: (y/x) = cx, where c is an arbitary constant Option 2: (y/x) = cx, where c is an arbitary constant Option 3: (x/y) = cx, where c is an arbitary constant Option 4: (y/x) = cx^2, where c is an arbitary constant

Answer: (y/x) = cx, where c is an arbitary constant. Solution: Solution Coming Soon

Calculus

Differential Equations

Medium

core

The general solution of the differential equation $x\left(\frac{dy}{dx}\right) = y + x \tan\left(\frac{y}{x}\right)$ is

$\tan\left(\frac{y}{x}\right) = cx$ , where c is an arbitary constant

$\sin\left(\frac{y}{x}\right) = cx$ , where c is an arbitary constant

$\sin\left(\frac{x}{y}\right) = cx$ , where c is an arbitary constant

$\sin\left(\frac{y}{x}\right) = cx^2$ , where c is an arbitary constant

✅ Correct Option: 2

Solution Coming Soon

2026: 22 May Shift 1

The particular solution of the differential equation $\log\left(\frac{dy}{dx}\right)=3x+4y$ , given that $y=0$ , when $x=0$ is:

2022: 30 Aug Shift 1

Solution of the differential equation $(x + xy)dy - y(1 - x^2)dx = 0$ is

2025: 30 May Shift 1

For the differential equation $ydx - (x + 3y^2)dy = 0$ , which of the following statements are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) If $y(0) = 1$ , then its particular solution is $x = 3y^2 - 1$

Choose the correct answer from the options given below:

2025: 13 May Shift 1

The particular solution of the differential equation $e^x\sqrt{1-y^2}dx + \frac{y}{x}dy = 0$ , given that $y = 1$ , when $x = 0$ is:

2026: 29 May Shift 1

Match List-I with List-II

List-I (Differential Equation)	List-II (Degree)
(A) $\left(\dfrac{dy}{dx}\right)^3+\left(\dfrac{d^2y}{dx^2}\right)^2=0$	(I) Not defined
(B) $\left(\dfrac{d^2y}{dx^2}\right)^3+\left(\dfrac{dy}{dx}\right)^2+1=0$	(II) 2
(C) $\sqrt{1+\dfrac{d^2y}{dx^2}}=\dfrac{dy}{dx}+x$	(III) 1
(D) $\dfrac{d^2y}{dx^2}+e^{\frac{dy}{dx}}=0$	(IV) 3

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

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