The product of the order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2 - 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^4$ is

Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :

consider the differential equation $\dfrac{dx}{dy} + Px = Q$, where $P$ and $Q$ are function of $y$. Then

A. Its integrating factor (I.F.) is $e^{\int Pdy}$

B. Its integrating factor (I.F.) is $e^{\int Pdx}$

C. Its solution is given by $x(I.F.) = \int Q(I.F.)dy + C$

D. Its solution is given by $y(I.F.) = \int Q(I.F.)dx + C$

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Match the LIST-I with LIST-II

[$a$ is an arbitrary constant]

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The differential equation of the family of curves $y = Ae^{3x} + Be^{-3 x}$, where $a$ and $\beta$ are arbitrary constants, is

Which of the following are correct?

(A) The order of the differential equation $\left(\dfrac{dy}{dx}\right)^2+3y^2-5y=0$ is 2.

(B) The degree of the differential equation $x\dfrac{d^2y}{dx^2}=\left(3+2\left(\dfrac{dy}{dx}\right)^2\right)^3$ is 3.

(C) The differential equation representing the curve $y=cx$, $c$ being an arbitrary constant is $ydx-xdy=0$.

(D) The general solution of an ordinary differential equation of $n^{th}$ order contains $n$ independent arbitrary constants.

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The particular solution of the differential equation x(1 + y²)dx - y(1 + x²)dy = 0, y(0) = 1, is: