Match List-I with List-II

List-I Differential equation	List-II Curve satisfying the differential equation
(A) $\frac{d^2y}{dx^2}+y=0$	(I) $x^2+y^2=C$: Where C is an arbitrary constant
(B) $\frac{dy}{dx}+y=\frac{x^2+y}{x}$	(II) $3e^{-4y}+4e^{3x}=C$: Where C is an arbitrary constant
(C) $\frac{dy}{dx}+\frac{x}{y}=0$	(III) $y=\sin x+\cos x+C$: Where C is an arbitrary constant
(D) $\log(dy/dx)=3x+4y$	(IV) $y=x+Cxe^{-x}$: Where C is an arbitrary constant

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Match List-I with List-II

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The general solution of the differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^x+e^{-x}}$ is

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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The equation of curve whose slope is given by $\frac{dy}{dx} = x$ and which passes through $\left(1, \frac{5}{2}\right)$ is :

Particular solution of the differential equation $\log\left(\frac{dy}{dx}\right) = x + y$, given that when $x = 0, y = 0$ is:

The integrating factor of the differential equation, $x^2 \frac{dy}{dx} + xy = log_e x$ is equal to