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

The answer is 'y = (1+x)_e(1+x) - x + 5'. View full solution:

CUET Mathematics - The solution of the differential equation e^dy/dx = x+1; y(0)=5 is | PYQs + Solutions

CUET Mathematics 2026 21st May Shift 1

Calculus

Medium

core

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

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

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

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

✅ Correct Option: 4

Related questions:

15 May Shift 1

Match List-I with List-II

List-I	List-II
(Differential equation)	(Order and Degree)
(A) $\frac{d^3y}{dx^3} + y^2 + e^{dy/dx} = 0$	(I) order = 3, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} + 1 = 0$	(II) order = 3, degree not defined
(C) $2x^2\frac{d^2y}{dx^2} - 3\left(\frac{dy}{dx}\right)^2 + y = 0$	(III) order = 2, degree = 3
(D) $\frac{d^3y}{dx^3} + 2\left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$	(IV) order = 2, degree = 1

Choose the correct answer from the options given below:

16 May Shift 1

For the differential equation $\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x$

(A) Degree of the given differential equation is $1$ .

(B) It is a homogeneous differential equation.

(C) Solution is $2y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}$ , where $A$ is an arbitrary constant

(D) Solution is $2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right)$ , where $A$ is an arbitrary constant

Choose the correct answer from the options given below :

15th 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: