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The solution of the differential equa...

The solution of the differential equation `(dy)/(dx)=(x+y)/x` satisfying the condition `y""(1)""=""1` is (1) `y""="ln"x""+""x` (2) `y""=""x"ln"x""+""x^2` (3) `y""=""x e(x-1)` (4) `y""=""x"ln"x""+""x`

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To solve the differential equation \(\frac{dy}{dx} = \frac{x+y}{x}\) with the condition \(y(1) = 1\), we will follow these steps: ### Step 1: Rewrite the differential equation The given differential equation can be rewritten as: \[ \frac{dy}{dx} = 1 + \frac{y}{x} \] ...
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