CUET Mathematics - The general solution of the differential equation dy/dx = e^x-y + x^2e^-y is equal to: | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 2

Calculus

Medium

applied

$e^y = e^x + \frac{x^3}{3} + c$ , where $c$ is an arbitrary constant.

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

$e^y = 2e^x + \frac{x^2}{4} + c$ , where $c$ is an arbitrary constant.

$y = e^x + \frac{x^3}{3} + c$ , where $c$ is an arbitrary constant.

✅ Correct Option: 1

Related questions:

2 June Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^3 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^2 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Choose the correct answer from the options given below:

21 May Shift 1

The differential equation representing the curve $y = e^{2x}(a + bx)$ , where a, b are arbitrary constants is

14 May Shift 1

Which of the following are linear first order differential equations?

(A) $\frac{dy}{dx} + P(x)y = Q(x)$

(B) $\frac{dx}{dy} + P(y)x = Q(y)$

(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$

Choose the correct answer from the options given below:

CUET Mathematics 2025 14 May Shift 2 PYQs