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The solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}-\frac{\mathrm{y}+3\mathrm{x}}{{\log }_{\math…

Q1

The solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}-\frac{\mathrm{y}+3\mathrm{x}}{{\log }_{\mathrm{e}}(\mathrm{y}+3\mathrm{x})}+3=0\) is: (where C is a constant of integration.)

[JEE Main 2020, 4 Sep (Shift 2)]

a

\(\mathrm{x}-\frac{1}{2}{\left({\log }_{\mathrm{e}}(\mathrm{y}+3\mathrm{x})\right)}^{2}=\mathrm{C}\)

b

\(\mathrm{y}+3\mathrm{x}-\frac{1}{2}{\left({\log }_{\mathrm{e}}\mathrm{x}\right)}^{2}=\mathrm{C}\)

c

\(\mathrm{x}-2{\log }_{\mathrm{e}}(\mathrm{y}+3\mathrm{x})=\mathrm{C}\)

d

\(\mathrm{x}-{\log }_{\mathrm{e}}(\mathrm{y}+3\mathrm{x})=\mathrm{C}\)

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