The differential equation satisfied by the equation y = ae^bx, where a and b are arbitrary constants, is Option 1: d^2y/dx^2 = y(dy/dx)^2 Option 2: yd^2y/dx^2 = (dy/dx)^2 Option 3: yd^2y/dx^2 = dy/dx Option 4: d^2y/dx^2 = ydy/dx

The answer is 'yd^2y/dx^2 = (dy/dx)^2'. View full solution:

CUET Mathematics - The differential equation satisfied by the equation y = ae^bx, where a and b are arbitrary constants, is | PYQs + Solutions

CUET Mathematics 2026 18th May Shift 1

Calculus

Medium

applied

$\frac{d^2y}{dx^2} = y\left(\frac{dy}{dx}\right)^2$

$y\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

$y\frac{d^2y}{dx^2} = \frac{dy}{dx}$

$\frac{d^2y}{dx^2} = y\frac{dy}{dx}$

✅ Correct Option: 2

Related questions:

21 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	General solution
---	---
(A) $\dfrac{dy}{dx} = \dfrac{y}{x}; x \neq 0$	(I) $y = cx; c \text{ is an arbitrary constant}$
(B) $x dx - y dy = 0; y \neq 0, x \neq 0$	(II) $x^2 - y^2 = c; c \text{ is an arbitrary constant}$
(C) $\dfrac{(x^2 - 1)}{y^2 + 1}\dfrac{dx}{dy} = 1$	(III) $2x + 3y = c; c \text{ is an arbitrary constant}$
(D) $2 dx + 3 dy = 0$	(IV) $(x^3-y^3) = c + 3(x+y); c \text{ is an arbitrary constant}$

Choose the correct answer from the options given below:

30th May Shift 1

Integrating factor of the differential equation $x\log x\frac{dy}{dx}+y=2\log x$ is equal to:

(Consider $\log x=\log_e x$ )

21st May Shift 1

For the differential equation $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} = k, k \neq 0$ , which one of the following is TRUE ?

CUET Mathematics 2026 18th May Shift 1 PYQs

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