Solve the separable differential equation for u. du/dt=e^(5u+2t). use initial condition u(0)=16

Answer 1

du/dt = e^5u·e^2t; ∫e^-5udu = ∫e^2tdt; - e^-5u/5 = e^2t/2 + C; - e^-80/5 = 1/2 + C ; C = -1/2 - 1/(5e⁸⁰)

e^2t/2 + e^-5u/5 = 1/2 + e^-80/5