If dy/dx = e^x-y + x^2e^-y, then the solution of the differential equation will be:- Option 1: e^y = e^x + x^2/2 + C, where C is an arbitrary constant Option 2: e^y = e^x + x^3/3 + C, where C is an arbitrary constant Option 3: e^y = e^x + 2x + C, where C is an arbitrary constant Option 4: e^y = e^x + 3x^2 + C, where C is an arbitrary constant

The answer is 'e^y = e^x + x^3/3 + C, where C is an arbitrary constant'. View full solution:

CUET Mathematics - If dy/dx = e^x-y + x^2e^-y, then the solution of the differential equation will be:- | PYQs + Solutions

CUET Mathematics 2026 26th May Shift 2

Calculus

Easy

applied

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

$e^y = e^x + \dfrac{x^3}{3} + C$ , where $C$ is an arbitrary constant

$e^y = e^x + 2x + C$ , where $C$ is an arbitrary constant

$e^y = e^x + 3x^2 + C$ , where $C$ is an arbitrary constant

✅ Correct Option: 2

Related questions:

22 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equation	Order and Degree
(A) $\left(\frac{d^2y}{dx^2}\right)^2 = e^x\left(\frac{dy}{dx}\right)^4 + 1 = 0$	(I) order = 1 and degree = 2
(B) $\left(\frac{dy}{dx}\right)^2 + xy = 0$	(II) order = 2 and degree = 1
(C) $\left(1 + \frac{dy}{dx}\right)^{3/2} = 4\left(\frac{d^2y}{dx^2}\right)^2$	(III) order = 2 and degree = 2
(D) $\sqrt\frac{d^2y}{dx^2} + 1 = \frac{dy}{dx}$	(IV) order = 2 and degree = 4

Choose the correct answer from the options given below:

15 May Shift 2

Consider the curve which is represented by the differential equation $\frac{dy}{dx} = 1 + x + y + xy$ . If it passes through the point $(0,0)$ , then which of the following is/are true?

(A) it is a straight line.

(B) it is a parabola.

(D) Its equation is $xy(x + 1)\left(y - \frac{1}{\sqrt{e}} + 1\right) = 0$

Choose the correct answer from the options given below:

2 June Shift 1

The solution of the differential equation $ydx + (x - y^2)dy = 0$ is

CUET Mathematics 2026 26th May Shift 2 PYQs

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