The slope at any point of a curve $y=f(x)$ is given by $\frac{dy}{dx}=3x^2$ and it passes through $(-1,1)$. The equation of the curve is

The rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. The temperature of air is $290 \ K$ and the substance cools from $370 \ K$ to $330 \ K$ in $10 \ minutes$. Then the time to cool the substance up to $295 \ K$ is: (in $min$)

The number of solutions of $\frac{dy}{dx} = \frac{y+1}{x-1}$,when $y(1) = 2$ is

$A$ body cools according to Newton's law of cooling from $100^{\circ} C$ to $60^{\circ} C$ in $20 \text{ minutes}$. If the temperature of the surrounding is $20^{\circ} C$,then the temperature of the body after one hour is: (in $^{\circ} C$)

If the general solution of the differential equation $y' = \frac{y}{x} + \phi \left( \frac{x}{y} \right)$,for some function $\phi$,is given by $y \ln |cx| = x$,where $c$ is an arbitrary constant,then $\phi(2)$ is equal to:

At any point $(x, y)$ of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point $(-4, -3)$. Find the equation of the curve given that it passes through $(-2, 1)$.