A curve satisfies dy/dx = (x + y)/x for x > 0, and it passes through the point (1, 2)…

Step 1. Substitute. With $y = vx$: $v + x\dfrac{dv}{dx} = 1 + v$. So $x\dfrac{dv}{dx} = 1$.

Step 2. Integrate. $v = \ln x + C$, so $y = x(\ln x + C)$.

Step 3. The constant. At $(1, 2)$: $2 = 1 \times (0 + C)$, so $C = 2$. The curve is $y = x(\ln x + 2)$.

Step 4. Evaluate. At $x = e$: $y = e(1 + 2) = 3e = 8.1548$. At $x = 2$: $y = 2(0.6931 + 2) = 5.3863$.