The solution of the differential equation e^(dy/dx) = x+1; y(0)=5 is Option 1: y = x_e x - x + 5 Option 2: y = x_e(1+x) - x Option 3: y = 2_e(1+x) + x Option 4: y = (1+x)_e(1+x) - x + 5

Answer: y = (1+x)_e(1+x) - x + 5. Solution: Taking logarithms, dy/dx=_e(1+x). Integrating by parts, y=(1+x)_e(1+x)-x+C. Using y(0)=5 gives C=5, so y=(1+x)_e(1+x)-x+5.

Calculus

Differential Equations

Medium

core

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$ ; $y(0)=5$ is

$y = x\log_e x - x + 5$

$y = x\log_e(1+x) - x$

$y = 2\log_e(1+x) + x$

$y = (1+x)\log_e(1+x) - x + 5$

✅ Correct Option: 4

Taking logarithms, $\frac{dy}{dx}=\log_e(1+x)$ . Integrating by parts, $y=(1+x)\log_e(1+x)-x+C$ . Using $y(0)=5$ gives $C=5$ , so $y=(1+x)\log_e(1+x)-x+5$ .

2026: 26 May Shift 2

The order and degree of the differential equation $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 2$ is

2023: 22 May Shift 3

The equation of curve whose slope is given by $\frac{dy}{dx} = x$ and which passes through $\left(1, \frac{5}{2}\right)$ is :

2025: 30 May Shift 1

The differential equation representing the family of curves $y = Ax + \frac{B}{x}$ , $x \neq 0$ where A and B are arbitrary constants, is given by

2026: 14 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:

2025: 15 May Shift 1

Consider the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ , then which of the following statements are correct?

(A) It is homogeneous

(B) It has $\sec x$ as its integrating factor

(D) It's degree is not defined

Choose the correct answer from the options given below:

2025: 15 May Shift 1

For $y \neq 0$ , the particular solution of the differential equation $2ye^{x/y}dx + (y - 2xe^{x/y})dy = 0$ at the point (1, 1) is

The solution of the differential equation edydx=x+1e^{\frac{dy}{dx}} = x+1edxdy​=x+1; y(0)=5y(0)=5y(0)=5 is

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CUET Mathematics Past Year Questions (Topic-Wise)

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$ ; $y(0)=5$ is