If the solution curve of the differentiable equation dy/dx + 2y = e^3x, passes through the point (0, 6/5), then the value of y(_e 2) is: Option 1: 37/20 Option 2: 1/5 Option 3: 11/5 Option 4: 1

Answer: 37/20. Solution: IF = e^2x. Solution: y * e^2x = e^5x dx = e^5x/5 + C. y = e^3x/5 + Ce^(-2x). At x=0: 6/5 = 1/5 + C, so C = 1. y( 2) = 8/5 + 1/4 = (32 + 5)/20 = 37/20.

Calculus

Differential Equations

Hard

If the solution curve of the differentiable equation $\frac{dy}{dx} + 2y = e^{3x}$ , passes through the point $\left(0, \frac{6}{5}\right)$ , then the value of $y(\log_e 2)$ is:

$\frac{37}{20}$

$\frac{1}{5}$

$\frac{11}{5}$

$1$

✅ Correct Option: 1

IF = $e^{2x}$ . Solution: $y \cdot e^{2x} = \int e^{5x} dx = \frac{e^{5x}}{5} + C$ .

$y = \frac{e^{3x}}{5} + Ce^{-2x}$ .

At $x=0$ : $\frac{6}{5} = \frac{1}{5} + C$ , so $C = 1$ .

$y(\log 2) = \frac{8}{5} + \frac{1}{4} = \frac{32 + 5}{20} = \frac{37}{20}$ .

2025: 14 May Shift 2

Particular solution of the differential equation $x(1 + y^2)dx - y(1 + x^2)dy = 0$ , given $y = 0$ when $x = 1$ , is

2023: 30 May Shift 3

If m and n are respectively the order and degree of the differential equation :

$\left(\frac{d^2 y}{dx^2}\right)^5 + 6 \frac{\left(\frac{d^2 y}{dx^2}\right)^3}{\frac{d^3 y}{dx^3}} + \frac{d^3 y}{dx^3} = x^2 + 5$ , then :

2025: 30 May Shift 1

The solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 5x + 2y$ is given by

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^{1/4} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^4 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

Choose the correct answer from the options given below:

2025: 3 June Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	Sum of order and degree
(A) $\frac{d^2y}{dx^2} + \frac{dy}{dx} + 3y = \sin x$	(I) 2
(B) $\frac{dy}{dx} = \sin(x + y)$	(II) 3
(C) $\sqrt{1 + (\frac{dy}{dx})^2} = \frac{d^2y}{dx^2}$	(III) 4
(D) $x^2(\frac{d^2y}{dx^2})^3 + y(\frac{dy}{dx})^4 + y^5 = 0$	(IV) 5

Choose the correct answer from the options given below:

2025: 14 May Shift 1

Which of the following are linear first order differential equations?

(A) $\frac{dy}{dx} + P(x)y = Q(x)$

(B) $\frac{dx}{dy} + P(y)x = Q(y)$

(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$

Choose the correct answer from the options given below:

If the solution curve of the differentiable equation dydx+2y=e3x\frac{dy}{dx} + 2y = e^{3x}dxdy​+2y=e3x, passes through the point (0,65)\left(0, \frac{6}{5}\right)(0,56​), then the value of y(log⁡e2)y(\log_e 2)y(loge​2) is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the solution curve of the differentiable equation $\frac{dy}{dx} + 2y = e^{3x}$ , passes through the point $\left(0, \frac{6}{5}\right)$ , then the value of $y(\log_e 2)$ is: