Find u\displaystyle {u} from the differential equation and initial condition.

dudt=e2.1t3.7u,  u(0)=2.4.\displaystyle \frac{{{d}{u}}}{{{\left.{d}{t}\right.}}}={e}^{{{2.1}{t}-{3.7}{u}}},\ \ {u}{\left({0}\right)}={2.4}.

u=\displaystyle {u}=