\(\text{ Let }y=y(x)\text{ be solution of the differential equation }{\log }_{e}\left(\frac{dy}{dx}\right)=3x+4y\text{, …

\(\text{ Let }y=y(x)\text{ be solution of the differential equation }{\log }_{e}\left(\frac{dy}{dx}\right)=3x+4y\text{, with }y(0)=0\text{. }\)

\(\text{ If }y\left(-\frac{2}{3}{\log }_{e}2\right)=\alpha {\log }_{e}2\text{, then the value of }\alpha \text{ is equal to: }\)

[JEE Main 2021, 27 Jul (Shift 1)]