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Question
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.
Solution
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = `1/sqrt(x)`.
Explanation:
`1/sqrt(x)`; the given equation can be written as
`"dy"/"dx" = ("e"^(-2sqrt(x)))/sqrt(x) - y/sqrt(x)`
i.e. `"dy"/"dx" + y/sqrt(x) = ("e"^(-2sqrt(x)))/sqrt(x)`
This is a differential equation of the type `"dy"/"dx" + "P"y` = Q.
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