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

The answer is 'e^y - e^x = x^3 + C'. View full solution:

CUET Mathematics - Solution of differential equation dy/dx = e^x-y + 3x^2 e^-y is: (where C is an arbitrary constant) | PYQs + Solutions

CUET Mathematics 2026 19th May Shift 2

Calculus

Easy

common

$e^y + e^x = x^3 + C$

$e^y - e^x = x^3 + C$

$e^{x-y} = x^3 + C$

$e^x - e^y = 3x^3 + C$

✅ Correct Option: 2

Related questions:

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:

29th May Shift 1

Which of the following are correct?

(A) The order of the differential equation $\left(\dfrac{dy}{dx}\right)^2+3y^2-5y=0$ is 2.

(B) The degree of the differential equation $x\dfrac{d^2y}{dx^2}=\left(3+2\left(\dfrac{dy}{dx}\right)^2\right)^3$ is 3.

(D) The general solution of an ordinary differential equation of $n^{th}$ order contains $n$ independent arbitrary constants.

Choose the correct answer from the options given below:

14th May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Differential Equation)		LIST-II (Order and degree)
A.	$\log\left(\dfrac{dy}{dx}\right) + \dfrac{d^2y}{dx^2} = 0$	I.	Order : 3 and degree : not defined
B.	$\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 4$	II.	Order : 2 and degree : 2
C.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dy}{dx} = \sqrt{x}$	III.	Order : 2 and degree : not defined
D.	$\left(1+\left(\dfrac{dy}{dx}\right)^2\right)^{3/2} = \dfrac{d^2y}{dx^2}$	IV.	Order : 2 and degree : 1

Choose the correct answer from the options given below: