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Question
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
Solution
Given differential equation is `log((dy)/(dx)) = ax + by`
⇒ `(dy)/(dx) = e^(ax + by)`
⇒ `(dy)/(dx) = e^(ax).e^(by)`
⇒ `(dy)/(e^(by)) = e^(ax) dx`
⇒ `e^(-by) dy = e^(ax) dx`
On integrating both sides, we get
`inte^(-by)dy = inte^(ax)dx`
`e^(-by)/(-b) = e^(ax)/a + C`
⇒ `e^(ax)/a - e^(-by)/b + C` = 0
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