Q: Solve dy/dx = x/y with y(1) = 2. Separate: y dy = x dx. Integrate: y^2/2 = x^2/2 + C, so y^2 = x^2 + C. Initial: 4 = 1 + C, C = 3. Solution: y^2 = x^2 + 3 (take y > 0: y = sqrt(x^2+3)).