Question

Solve the differential equation:

`"dy"/"dx" = 2^(-"y")`

Answer 1

Given differential equation is

`"dy"/"dx" = 2^(-"y")`

On separating the variables, we get

`"dy"/(2^(-"y"))` = dx

⇒ 2^y dy = dx

On integrating both sides, we get

`∫ 2^"y" "dy" = ∫ "dx"`

⇒ `(2^"y")/(log 2) = "x" + "c"_1`

⇒ 2^y = x log 2 + c₁ log 2

∴ 2^y = x log 2 + c

where c = c₁ log 2