Find the solution of `(dy)/(dx)=2^(y-x)`

Explanation

`"Given that",=(dy)/(dx)=2^(y-x)`
`Rightarrow (dy)/(dx)=(2^(y))/(2^(x))[therefore 2^(m-n)=(a^(m))/(a^(n))]`
`Rightarrow (dy)/(2^(y))=(dx)/(2^(x))`
On integrating both sides, we get
`int2^(-y)dy=int2^(-x)dx`
`Rightarrow (-2^(-y))/(log2)=(-2^(-x))/(log2)+C`
`Rightarrow -2^(-y)+2^(-x)=+Clog2`
`Rightarrow 2^(-x)+2^(-y)=-Clog2`
`Rightarrow 2^(-x)+2^(-y)=K`