Match List-I with List-II

List-I Differential equation	List-II Order and degree
(A) $\frac{d^4y}{dx^4} + \sin\left(\frac{d^3y}{dx^3}\right) = 0$	(I) order = 2, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = 0$	(II) order = 3, degree = 1
(C) $\frac{d^3y}{dx^3} + y^2 + \frac{dy}{dx} = 0$	(III) order = 2, degree = 2
(D) $3y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^4 = 0$	(IV) order = 4, degree not defined

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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

Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$ be $m$ and $n$ respectively. Then

(A) m = 2

(B) n = 3

(C) m = 3

(D) mn = 4

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Match List-I with List-II

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The general solution of the differential equation $\tan\left(\dfrac{(1+x^2)y'+2xy}{2x}\right)=1+x^2$, is

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

(where C is an arbitrary constant)

The differential equation $y = xp + \sqrt{x^2 p^3 + 4}$ where $p = \frac{dy}{dx}$ is :

(A) of order 1

(B) of degree 1

(C) of order 2

(D) of degree 3

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The solution of the differential equation $\frac{dy}{dx} = \frac{\lambda^2}{(x+y)^2}$ ($\lambda$ is constant) is: