A) \[y={{x}^{2}}\]
B) \[{{x}^{2}}-{{y}^{2}}=0\]
C) \[2{{x}^{2}}+{{y}^{2}}=3\]
D) None of these
Correct Answer: A
Solution :
Slope \[\frac{dy}{dx}=\frac{2y}{x}\] Þ \[2\int{\frac{dx}{x}}=\int{\frac{dy}{y}}\] Þ \[2\log x=\log y+\log c\] Þ \[{{x}^{2}}=yc\] Since it passes through (1, 1), therefore \[c=1\] Hence \[{{x}^{2}}-y=0\] Þ \[y={{x}^{2}}\].
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