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 $y(I.F.) = \int Q(I.F.)dx + C$

Choose the correct answer from the options given below:

The differential equation representing family of circles with centre at origin and radius r units 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 :

The degree of the differential equation

$\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

The solution of $y' - y'' = 2x$ is:

A. $y = x^2 + 2x + 2$

B. $y = x^2 + 2x + 1$

C. $y = x + 2$

D. $y = x^2 - 2x + 1$

Choose the correct answer from the options given below:

The general solution of the differential equation $\frac{dy}{dx} = e^{x-y} + x^2e^{-y}$ is equal to:

The general solution of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$