10 Multiple Choice 1 point Solve the differential equation: \( y^{\prime}=(\sqrt{x}) /(2 y) \) \( y=(2 / 3) x^{\wedge}(3 / 2)+C \) \( y^{\wedge} 2=(3 / 2) x^{\wedge}(2 / 3)+C \) \( y^{\wedge} 2=(2 / 3) x^{\wedge}(3 / 2)+C \) \( y=(3 / 2) x^{\wedge}(2 / 3)+C \)

To solve the differential equation \( y' = \frac{\sqrt{x}}{2y} \), you can separate variables. Rearranging gives \( 2y \, dy = \sqrt{x} \, dx \). Integrating both sides, you’d find \( y^2 = \frac{2}{3}x^{3/2} + C \). A little rearranging would put it in a more standard form. Remember, integrating with care and checking your work is crucial! In practical terms, this equation can model situations where quantities grow in relation to each other, like populations or chemical reactions. Understanding how to solve these equations can be useful in fields ranging from biology to engineering, where predicting changes over time is key! So whether you're calculating the trajectory of a rocket or the spread of a virus, this technique can come in quite handy!