JEE MAIN - Mathematics Hindi (2023 - 25th January Morning Shift - No. 14)
माना अवकल समीकरण $$\frac{d y}{d x}=\frac{y}{x}\left(1+x y^{2}\left(1+\log _{e} x\right)\right), x > 0, y(1)=3$$ का
हल $$y=y(x)$$ है । तो $$\frac{y^{2}(x)}{9}$$ बराबर है :
$$\frac{x^{2}}{5-2 x^{3}\left(2+\log _{e} x^{3}\right)}$$
$$\frac{x^{2}}{3 x^{3}\left(1+\log _{e} x^{2}\right)-2}$$
$$\frac{x^{2}}{7-3 x^{3}\left(2+\log _{e} x^{2}\right)}$$
$$\frac{x^{2}}{2 x^{3}\left(2+\log _{e} x^{3}\right)-3}$$
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