Question

Solve the separable differential equation for u : du/dt =e^(6u+6t) use the following initial condition u(0)=10

Answer 1

e^(-6u) du=e^(6t)dt
e^(-6u)/-6=e^(6t)+C
puting intial condition
e^(-60)/-6=1+C
so C=-(1+1/6e^(60))

Answer 2

but i need to solve to u not just c

Answer 3

you can write like that
e^(-6u)=-6e^(6t)-6C
take anti log on both side
-6u=ln(-6e^(6t)-6C)
u=ln(1/(-6e^(6t)-6C)^6)

Answer 4

is not right :(