Let \(y = y(x)\) be solution of the differential equation \({\log }_{\mathrm{e}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\ri…

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

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