Statement-1: Curve satisfying the differential
equation $y^{'} = y / 2 x$ passing through (2, 1) is a parabola
with focus (1/4, 0)
Statement-2: The differential equation $y^{'} = y / 2 x$ is of variable
separable.

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

answer is D.

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Detailed Solution

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

$\log y^{2} = \log x + const \Rightarrow y^{2} = C x$ , this passes through
(2, 1) if $C = 1 / 2$ . Thus $y^{2} = 1 / 2 x$ which represents a parabola

with focus (1/8, 0).

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