The general solution of the given differential equation $dy + (2y - e^{-2x})dx = 0$, is:

[where c is an arbitrary constant]

Match the LIST-I with LIST-II

[$a$ is an arbitrary constant]

Choose the correct answer from the options given below:

The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are

The product of order and degree of the differential equation

$x\dfrac{d^3y}{dx^3} = \left(1 + \left(\dfrac{dy}{dx}\right)^2\right)^4$ 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 :

The solution of the differential equation $\frac{dy}{dx} + y = 1, y(1) = 0$ is

The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is