Solve the separable differential equation for u\displaystyle {u}

dudt=e5u+6t.\displaystyle \frac{{{d}{u}}}{{{\left.{d}{t}\right.}}}={e}^{{{5}{u}+{6}{t}}}.

Use the following initial condition: u(0)=4\displaystyle {u}{\left({0}\right)}={4}.

u=\displaystyle {u}=