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

Answer

Given differential equation is
$\frac{d y}{d x}=2^{-y}$
On separating the variables, we get
$2^y d y=d x$
On integrating both sides, we get c
$\int 2^y d y=\int d x$
or $\frac{2^y}{\log 2}=x+C_1$
or $2^y=x \log 2+C_1 \log 2$
$\therefore 2^y=x \log 2+C$, where $C=C_1 \log 2$

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