Question

Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .

Answer 1

We have

\[\frac{dy}{dx} = 2^{- y} \]

\[ \Rightarrow \frac{dy}{2^{- y}} = dx\]

\[ \Rightarrow 2^y dy = dx\]

Integrating both sides, we get

\[\int 2^y dy = \int dx\]

\[ \Rightarrow \frac{2^y}{\log2} = x + c\]

\[ \Rightarrow 2^y = x\log2 + k, \text { where } k = c\log2\]