If \( \frac{d y}{d x}=\frac{y^{3}}{e^{2 x}+y^{2}} \) and \( y(0)=1 \), then: (a) \( y^{2}=e^{2 x...

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If \( \frac{d y}{d x}=\frac{y^{3}}{e^{2 x}+y^{2}} \) and \( y(0)=1 \), then:
(a) \( y^{2}=e^{2 x}-2 e^{2 x} \ln y \)
(b) \( y^{2}=e^{2 x}+2 e^{2 x} \ln y \)
(c) \( y^{2}=e^{2 x}-\frac{1}{2} e^{2 x} \ln y \)
(d) \( y^{2}=e^{2 x}+\frac{1}{2} e^{2 x} \ln y \)
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