Solution of differential equation dy/dx = e^(x+y) - xe^y is Option 1: e^x + e^y - x^2/2 = C, where C is an arbitrary constant Option 2: e^x + e^(-y) - x^2/2 = C, where C is an arbitrary constant Option 3: e^x + e^y + x^2/2 = C, where C is an arbitrary constant Option 4: e^x - e^(-y) - x^2/2 = C, where C is an arbitrary constant

Answer: e^x + e^(-y) - x^2/2 = C, where C is an arbitrary constant. Solution: Factorise: dy/dx = e^y(e^x-x), so e^(-y)dy = (e^x-x)dx. Integrating: -e^(-y) = e^x-x^2/2+C_1. Rearranging gives e^x+e^(-y)-x^2/2 = C.

Calculus

Differential Equations

Medium

common

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

$e^x + e^y - \frac{x^2}{2} = C$ , where C is an arbitrary constant

$e^x + e^{-y} - \frac{x^2}{2} = C$ , where C is an arbitrary constant

$e^x + e^y + \frac{x^2}{2} = C$ , where C is an arbitrary constant

$e^x - e^{-y} - \frac{x^2}{2} = C$ , where C is an arbitrary constant

✅ Correct Option: 2

Factorise: $\frac{dy}{dx} = e^y(e^x-x)$ , so $e^{-y}dy = (e^x-x)dx$ .

Integrating: $-e^{-y} = e^x-\frac{x^2}{2}+C_1$ .

Rearranging gives $e^x+e^{-y}-\frac{x^2}{2} = C$ .

2024: 16 May Shift 1

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

2026: 15 May Shift 1

If $p$ and $q$ are degree and order of the differential equation $\left(\dfrac{d^2y}{dx^2}\right)^3 - 2\left(\dfrac{dy}{dx}\right)^4 = 6$ respectively. Then the value of $2p+3q$ is

2026: 15 May Shift 1

If $c$ is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I (Differential Equation)		LIST-II (Solution)
A.	$\dfrac{dy}{dx} = 1 + x + y + xy$	I.	$\log_e \vert y \vert = 2x + \log_e (x-1)^2 + c$
B.	$(x-1)\dfrac{dy}{dx} = 2xy$	II.	$y = cx$
C.	$\dfrac{dy}{dx} = 1 - x + y - xy$	III.	$\log_e \vert 1+y \vert = x + \dfrac{x^2}{2} + c$
D.	$x\,dy = y\,dx$	IV.	$\log_e \vert 1+y \vert = x - \dfrac{x^2}{2} + c$

Choose the correct answer from the options given below:

2025: 3 June Shift 2

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

2025: 3 June Shift 1

The particular solution of the differential equation $xdy = (2x^2 + 1)dx, x \neq 0$ , given that $y = 1$ when $x = 1$ is:

2022: 16 July Shift 2

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

Solution of differential equation dydx=ex+y−xey\frac{dy}{dx} = e^{x+y} - xe^ydxdy​=ex+y−xey is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

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