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Question
Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.
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Solution
Given `"dy"/"dx" = y + y/x`
= `"y"(1 + 1/x)`
⇒ `"dy"/y = (1 + 1/x)"d"x`
Integrating both sides, we get
logy = x + logx + c
⇒ `log(y/x)` = x + c
⇒ `y/x = "e"^(x + "c") `
= `"e"^x * "e"^"c"`
⇒ `y/x` = k . ex
⇒ y = kx . ex.
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