Question

Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.

Answer 1

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 . e^x

⇒ y = kx . e^x.