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Equation of the curve passing through (1, 1} and satisfying the differential equation $\frac{d y}{d x} = \frac{2 y}{x}$ , $(x > 0, y > 0)$ is given by

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y = 2x

$x^{2} = y$

$x = y^{2}$

x = 2y

answer is A.

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Detailed Solution

$\frac{d y}{d x} = \frac{2 y}{x}$

$\begin{array}{l} \Rightarrow \frac{1}{y} d y = \frac{2}{x} d x \\ ∴ \log y = \log x^{2} + c \end{array}$

where c = 0 as it passes through (1,1)

$\Rightarrow x^{2} = y$

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