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

Answer: 2e^y=e^2x+x^2+C: where C is an arbitrary constant. Solution: Write dy/dx=e^(-y)(e^2x+x) and separate variables: e^ydy=(e^2x+x)dx. Integrating gives e^y=e^2x/2+x^2/2+C', i.e. 2e^y=e^2x+x^2+C.

Calculus

Differential Equations

Easy

common

The general solution of the differential equation $\frac{dy}{dx}=e^{2x-y}+xe^{-y}$ is:

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

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

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

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

✅ Correct Option: 2

Write $\frac{dy}{dx}=e^{-y}(e^{2x}+x)$ and separate variables: $e^{y}dy=(e^{2x}+x)dx$ .

Integrating gives $e^{y}=\frac{e^{2x}}{2}+\frac{x^2}{2}+C'$ , i.e. $2e^{y}=e^{2x}+x^2+C$ .

2025: 14 May Shift 1

Consider the differential equation, $x\frac{dy}{dx} = y(\log_e y - \log_e x + 1)$ , then which of the following are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) Its general solution is $\log_e\left(\frac{x}{y}\right) = Cy$ , where C is constant of integration

(E) If $y(1) = 1$ , then its particular solution is $y = x$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

2025: 22 May Shift 1

Which of the following statements is/are true?

(A) $(\tan^{-1} y - x)dy = (1 + y^2)dx$ is a differential equation where variables are separable.

(B) $(1 + x^2)dy + 2xydy = \cot x \ dx (x \neq 0)$ is a first order linear differential equation.

(D) $(xy)dx - (x + y^2)dy = 0$ is a homogeneous differential equation.

Choose the correct answer from the options given below:

2025: 19 May Shift 1

Solution of the differential equation

$\frac{dy}{dx} = \sqrt{1 + x^2 + y^2 + x^2y^2}$ is : (Here $C$ is an arbitrary constant)

2026: 31 May Shift 2

Match the LIST-I with LIST-II

[ $a$ is an arbitrary constant]

	LIST-I Differential Equation		LIST-II Family of curves
A.	$x\,dy - y\,dx = 0$	I.	$x^2 + y^2 = a^2$
B.	$2y\,dx - x\,dy = 0$	II.	$y = ax$
C.	$x\,dx + y\,dy = 0$	III.	$y^2 = 16x + a$
D.	$y\,dy - 8\,dx = 0$	IV.	$x^2 = ay$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Sum of order and degree)
A.	$(y'')^3 + xy' + 2y = 0$	I.	$6$
B.	$(y'')^2 + (y')^3 + 4y = 0$	II.	$3$
C.	$y'' + (y')^2 + 5y = 0$	III.	$4$
D.	$(y'')^4 + 3x(y')^2 + y = 0$	IV.	$5$

Choose the correct answer from the options given below:

The general solution of the differential equation dydx=e2x−y+xe−y\frac{dy}{dx}=e^{2x-y}+xe^{-y}dxdy​=e2x−y+xe−y is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The general solution of the differential equation $\frac{dy}{dx}=e^{2x-y}+xe^{-y}$ is: