Discussion
The general solution of the differential equation \(\dfrac{dy}{dx} - 2\sqrt{y} = 0\) is
Answer: D
The general solution is \(\sqrt{y} - x + C = 0\).
The equation is separable:
\[ \begin{aligned} \frac{dy}{dx} &= 2\sqrt{y} \\ \frac{dy}{2\sqrt{y}} &= dx \\ \sqrt{y} &= x + c \end{aligned} \]
since the derivative of \(\sqrt{y}\) is \(1/(2\sqrt{y})\). Moving everything to one side gives \(\sqrt{y} - x + C = 0\) with \(C = -c\).
The other forms fail when differentiated: \(y = x - C\) gives \(dy/dx = 1\), and any form with \(\sqrt{x}\) produces a derivative depending on x, which the equation does not have.
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