A body cools from $100^\circ\text{C}$ to $60^\circ\text{C}$ in 20 minutes, the temperature of the surroundings being $20^\circ\text{C}$. The total time taken (in minutes) for the body to cool down to $40^\circ\text{C}$ is ...

The general solution of the differential equation $x\sin x\dfrac{dy}{dx} + (x\cos x + \sin x)y = \sin x$ is

The general solution of the differential equation $\sec y + (x - e^{\sin y})\dfrac{dy}{dx} = 0$ is...

The general solution of the differential equations $\dfrac{dy}{dx} = (9x + y + 5)^2$ is...