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The solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=-\left(\frac{{\mathrm{x}}^{2}+3{\mathrm{y}}^…

Q1

The solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=-\left(\frac{{\mathrm{x}}^{2}+3{\mathrm{y}}^{2}}{3{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}\right),\mathrm{y}(1)=0\) is

[JEE Main 2023, 30 Jan (Shift 2)]

a

\({\log }_{\mathrm{e}}\left|\mathrm{x}+\mathrm{y}\right|-\frac{\mathrm{xy}}{(\mathrm{x}+\mathrm{y}{)}^{2}}=0\)

b

\({\log }_{\mathrm{e}}\left|\mathrm{x}+\mathrm{y}\right|+\frac{\mathrm{xy}}{(\mathrm{x}+\mathrm{y}{)}^{2}}=0\)

c

\({\log }_{\mathrm{e}}\left|\mathrm{x}+\mathrm{y}\right|+\frac{2\mathrm{xy}}{(\mathrm{x}+\mathrm{y}{)}^{2}}=0\)

d

\({\log }_{\mathrm{e}}\left|\mathrm{x}+\mathrm{y}\right|-\frac{2\mathrm{xy}}{(\mathrm{x}+\mathrm{y}{)}^{2}}=0\)

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