Mathematics

Mathematics

Problem

The solution of the differential equation dydx=−(x2+3y23x2+y2)\frac{dy}{dx} = -\left(\frac{x^2 + 3y^2}{3x^2 + y^2}\right), y(1)=0y(1) = 0 is: [JEE MAINS - ONLINE - 2023] (1) log⁡e∣x+y∣−xy(x+y)2=0\log_e |x + y| - \frac{xy}{(x + y)^2} = 0 (2) log⁡e∣x+y∣+xy(x+y)2=0\log_e |x + y| + \frac{xy}{(x + y)^2} = 0 (3) log⁡e∣x+y∣+2xy(x+y)2=0\log_e |x + y| + \frac{2xy}{(x + y)^2} = 0 (4) log⁡e∣x+y∣−2xy(x+y)2=0\log_e |x + y| - \frac{2xy}{(x + y)^2} = 0

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