A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area ?

The solution of $\dfrac{\text{d}y}{\text{d}x} = \sin(x + y) + \cos(x + y)$ is

The order and degree of the differential equation $3 - \left(\dfrac{\text{d}^3 y}{\text{d}x^3}\right)^{\frac{7}{3}} = \left(\dfrac{\text{d}y}{\text{d}x}\right)^5$ are respectively

The solution of the differential equation $e^{-x}(y+1)\text{d}y + (\cos^2 x - \sin 2x)y\, \text{d}x = 0$, given that $y = 1$ when $x = 0$ is