The sum of the degree and order of the differential equation $\sqrt{\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}}=\sqrt[5]{\frac{\mathrm{d} y}{\mathrm{~d} x}-5}$ is

The differential equation whose solution represents the family $x^2 y=4 \mathrm{e}^x+\mathrm{c}$, where c is an arbitrary constant, is

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is

For a perfectly black body, coefficient of emission is