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Question
Solve the differential equation:
`"dy"/"dx" = 2^(-"y")`
Solution
Given differential equation is
`"dy"/"dx" = 2^(-"y")`
On separating the variables, we get
`"dy"/(2^(-"y"))` = dx
⇒ 2y dy = dx
On integrating both sides, we get
`∫ 2^"y" "dy" = ∫ "dx"`
⇒ `(2^"y")/(log 2) = "x" + "c"_1`
⇒ 2y = x log 2 + c1 log 2
∴ 2y = x log 2 + c
where c = c1 log 2
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