CUET Mathematics - If e^y = x, then which of the following is true? | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 1

Calculus

Hard

applied

$x\frac{d^2y}{dx^2} - \left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$

$\frac{d^2y}{dx^2} - x\frac{dy}{dx} = 0$

$\frac{d^2y}{dx^2} - \left(\frac{dy}{dx}\right)^2 + 1 = 0$

$x\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$

✅ Correct Option: 4

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The sum of order and degree of the differential equation $(y^2\frac{d^2y}{dx^2})^{3/4} = 5(\frac{dy}{dx})^5 - 4$ is equal to

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Match List-I with List-II

List-I	List-II
Differential Equation	Order and degree of differential equation
(A) $\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^2 = e^{\frac{dy}{dx}} + 1$	(I) Order = 1, Degree = 2
(B) $\left(\frac{d^2y}{dx^2}\right)^2 + 4\left(\frac{dy}{dx}\right)^3 = e^y - 1$	(II) Order = 2, Degree = 1
(C) $3\left(\frac{dy}{dx}\right) + 4y + e^y = \frac{dx}{dy}$	(III) Order = 2, Degree = 2
(D) $\frac{d^2y}{dx^2} + 3\left(\frac{dy}{dx}\right) = \left(e^y + \frac{dy}{dx}\right)^2$	(IV) Order = 2, Degree = Not defined

Choose the correct answer from the options given below:

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CUET Mathematics 2025 14 May Shift 1 PYQs