CUET Mathematics 2025 - The product of order and degree of the differential equation (d^3y/dx^3)^2 + x^2y(d^2y/dx^2)^3 = 2x^5 is: | PYQs + Solutions

2025: 29 May Shift 2

For the differential equation $x\frac{dy}{dx} + 3y = x^2\log_e x$ , which of the following statements are TRUE?

(A) Product of order and degree is 1

(B) Integrating factor is $x^3$

(C) Integrating factor is $3x$

(D) General solution is $y = \frac{x^3}{36}(6\log_e|x| - 1) + Cx^{-3}$ , C is an arbitrary constant.

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2025: 13 May Shift 1

Match List-I with List-II

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2026: 12 May Shift 2

Which of the following differential equations has $y=x$ as one of the particular solution?

2026: 29 May Shift 1

Match List-I with List-II

List-I (Differential Equation)	List-II (Degree)
(A) $\left(\dfrac{dy}{dx}\right)^3+\left(\dfrac{d^2y}{dx^2}\right)^2=0$	(I) Not defined
(B) $\left(\dfrac{d^2y}{dx^2}\right)^3+\left(\dfrac{dy}{dx}\right)^2+1=0$	(II) 2
(C) $\sqrt{1+\dfrac{d^2y}{dx^2}}=\dfrac{dy}{dx}+x$	(III) 1
(D) $\dfrac{d^2y}{dx^2}+e^{\frac{dy}{dx}}=0$	(IV) 3

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2026: 18 May Shift 1

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$ ; $x \neq 0$ with $y = 1$ when $x = 1$ , is

2026: 12 May Shift 2

The general solution of the differential equation $ydx + (x-y^3)dy = 0$ is :

The product of order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2 + x^2y\left(\frac{d^2y}{dx^2}\right)^3 = 2x^5$ is: