The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm , after 2 minutes its radius becomes 9 cm , then radius of balloon after 4 minutes is

The integrating factor of $y+\frac{\mathrm{d}}{\mathrm{d} x}(x y)=x(\sin x+\log x)$ is

The differential equation whose solution is $\mathrm{A} x^2+\mathrm{B} y^2=1$, where A and B are arbitrary constants is of