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

Answer: 2^x + 2^(-y) = c where c is an arbitrary constant. Solution: Write dy/dx=2^x * 2^y and separate: 2^(-y)dy=2^x dx. Integrating gives -(2^(-y))/(_e 2)=2^x/(_e 2)+k, which rearranges to 2^x+2^(-y)=c.

Calculus

Differential Equations

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The solution of the differential equation $\dfrac{dy}{dx} = 2^{x+y}$ is

$2^x + 2^{-y} = c$ where $c$ is an arbitrary constant

$2^x + 2^y = c$ where $c$ is an arbitrary constant

$2^x - 2^{-y} = c$ where $c$ is an arbitrary constant

$2^x \times 2^y = c$ where $c$ is an arbitrary constant

✅ Correct Option: 1

Write $\frac{dy}{dx}=2^x \cdot 2^y$ and separate: $2^{-y}dy=2^x dx$ . Integrating gives $-\frac{2^{-y}}{\log_e 2}=\frac{2^x}{\log_e 2}+k$ , which rearranges to $2^x+2^{-y}=c$ .

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Sum of the order and the degree of the differential equation
A.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$	I.	$2$
B.	$4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$	II.	$3$
C.	$x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$	III.	$5$
D.	$\dfrac{dy}{dx} = x^4 e^{-3y}$	IV.	$4$

Choose the correct answer from the options given below:

2026: 12 May Shift 2

The general solution of the differential equation $ydx + (x-y^3)dy = 0$ is :

2025: 14 May Shift 2

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

2025: 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:

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
Differential equation	Order and degree
(A) $y''' + x^2(y'')^3 + y = 0$	(I) $3, 2$
(B) $y''' + y^2 + e^{y'} = 0$	(II) $3, 3$
(C) $(y''')^2 + x^2(y'')^3 + xy = 0$	(III) $3, 1$
(D) $(y''')^3 + x(y'')^2 + y = 0$	(IV) $3, \text{Not defined}$

Choose the correct answer from the options given below:

2025: 15 May Shift 2

The general solution of the differential equation $\frac{xdy}{dx} + 4y = x^3, (x \neq 0)$ is:

The solution of the differential equation dydx=2x+y\dfrac{dy}{dx} = 2^{x+y}dxdy​=2x+y is

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The solution of the differential equation $\dfrac{dy}{dx} = 2^{x+y}$ is