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

Answer: ^(-1)y/x = 1/2_e(x^2 + y^2) + C: C is an arbitrary constant. Solution: Solution Coming Soon

Calculus

Differential Equations

Medium

core

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

$y = \frac{x}{2}\log_e(x^2 + y^2) + C$ : C is an arbitary constant

$y = \sqrt{x^2 + y^2} + C$ : C is an arbitrary constant

$y = \frac{1}{2}\log_e(x^2 + y^2) + c$ : C is an arbitrary constant

$\tan^{-1}\frac{y}{x} = \frac{1}{2}\log_e(x^2 + y^2) + C$ : C is an arbitrary constant

✅ Correct Option: 4

Solution Coming Soon

2026: 31 May Shift 2

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Integrating factor
A.	$\dfrac{dy}{dx} + 3y = e^{-2x}$	I.	$\dfrac{1}{x}$
B.	$x\dfrac{dy}{dx} + y = 3x^2$	II.	$e^{-x}$
C.	$x\dfrac{dy}{dx} - y = 3x^2$	III.	$x$
D.	$\dfrac{dy}{dx} - y = x$	IV.	$e^{3x}$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

Given differential equation, (1 + y²)dx = (tan⁻¹y - x)dy, then which of the following is/are true?

(A) Integrating factor = tan⁻¹x

(B) Integrating factor = tan⁻¹y

(D) Degree = 1

Choose the correct answer from the options given below:

2024: 16 May Shift 1

If $\sin y=x \sin (a+y)$ , then $\frac{d y}{d x}$ is :

2025: 14 May Shift 2

Particular solution of the differential equation $x(1 + y^2)dx - y(1 + x^2)dy = 0$ , given $y = 0$ when $x = 1$ , is

2025: 13 May Shift 2

The general solution of differential equation $\frac{dy}{dx} = e^{x+y}$ is

2025: 3 June Shift 2

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$ , where m is arbitrary constant, is