Let \( y=y(x) \) be solution of the differential equation \( \log_{e}\!\left(\frac{dy}{dx}\right)=3x+4y \), with \( y(0)=0 \). If \( y\!\left(-\frac{2}{3}\log_{e}2\right)=\alpha \log_{e}2 \), then the value of \( \alpha \) is equal to:
\( \frac{1}{4} \)
\( 2 \)
\( -\frac{1}{2} \)
\( -\frac{1}{4} \)
