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Question
Solve: `log(("d"y)/("d"x))` = ax + by
Solution
`log(("d"y)/("d"x))` = ax + by
`(("d"y)/("d"x)) = "e"^("a"x + "b"y)`
`("d"y)/("d"x) = "e"^("a"x)* "e"^("b"y)`
⇒ `("d"y)/"e"^("b"y) = "e"^("a"x) "d"x`
⇒ `"e"^("a"x) "d"x = "e"^(-"b"y) "d"y`
Integrating on both sides
`int "e"^("a"x) "d"x = int "e"^(-"b"y) "d"y`
`"e"^("a"x)/"a" = "e"^(-"b"y)/(-"b") + "c"`
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