Write the solution of the differential equation ${\frac{d y}{d x}}=2^{-y}.$

Write the integrating factor of the differential equations ${\sqrt{x}}{\frac{d y}{d x}}+y=e^{-2{\sqrt{x}}}\,.$

Find the integrating factor of the differential equation

Write the integrating factor of the following differential equation. $(1+y^{2})+(2x y-\mathrm{cot}\;y){\frac{d y}{d x}}\;=0$