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

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

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