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(D) Given the differential equation: $y^{\prime} = \frac{y}{2x}$ Separating the variables, we get: $\frac{dy}{y} = \frac{dx}{2x}$ Integrating both sid

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parabolas

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(D) Given the differential equation: $y^{\prime} = \frac{y}{2x}$ Separating the variables, we get: $\frac{dy}{y} = \frac{dx}{2x}$ Integrating both sides: $\int \frac{1}{y} dy = \frac{1}{2} \int \frac{1}{x} dx$ $\ln|y| = \frac{1}{2} \ln|x| + C$ $\ln|y| = \ln|x^{1/2}| + C$ Taking the exponential of both sides: $y = k \sqrt{x}$, where $k = e^C$ Squaring both sides: $y^2 = k^2 x$ Let $k^2 = c$, then $y^2 = cx$ This equation represents a family of parabolas opening along the $x$-axis.

The family of curves represented by the general solution of $y^{\prime}=\frac{y}{2x}$ contains

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