CUET Mathematics 2025 - The sum of order and degree of the differential equation (x^2d^2y/dx^2)^(3/4) = 5(dy/dx)^2 - 3 is equal to | PYQs + Solutions

2026: 30 May Shift 2

If $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$ , then the order and degree of the differential equation are

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

2025: 15 May Shift 2

The general solution of the differential equation $\frac{xdy}{dx} + 4y = x^3, (x \neq 0)$ is:

2025: 14 May Shift 2

Match List-I with List-II

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

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2026: 14 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

2026: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $y + \frac{dy}{dx} = \frac{1}{4}\int y\,dx$	(I) Order 1, Degree 1
(B) $y = \frac{dy}{dx} + \frac{C}{dy/dx}$	(II) Order 2, Degree 2
(C) $(xy^2+x)dx + (y-x^2)dy = 0$	(III) Order 2, Degree 1
(D) $\left[\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2}/\frac{d^2y}{dx^2}\right] = K$	(IV) Order 1, Degree 2

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