The solution of differential equation \( x^{2}= \) \( 1+\left(\frac{x}{y}\right)^{-1} \frac{d y}...

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The solution of differential equation \( x^{2}= \) \( 1+\left(\frac{x}{y}\right)^{-1} \frac{d y}{d x}+\frac{\left(\frac{x}{y}\right)^{-2}\left(\frac{d y}{d x}\right)^{2}}{2 !}+\frac{\left(\frac{x}{y}\right)^{-3}\left(\frac{d y}{d x}\right)^{3}}{3 !}+\ldots \) is
(a) \( y^{2}=x^{2}\left(\ln x^{2}-1\right)+c \)
(b) \( y=x^{2}(\ln x-1)+c \)
(c) \( y^{2}=x(\ln x-1)+c \)
(d) \( y=x^{2} e^{x^{2}}+c \)
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