Question

solve the separable differential equation for u: du/dt=e^(6u+3t) use the following initial condition: u(0)=12 so u(t)=?

Answer 1

if its separable; then separate :)

Answer 2

e^(a+b) = e^a e^b

Answer 3

is this a differential equations course?

Answer 4

e^6u+e^3t like that

Answer 5

not the "+" between it, that i can see

Answer 6

so du/e^(6u)=e^(3t)+dt

Answer 7

there should be no "+" sign in either case lol

Answer 8

its just a chapter were going through for calculus 2

Answer 9

\[\int\limits_{}^{}\frac{1}{e^{6u}} du=\int\limits_{}^{}e^{3t}dt\]

Answer 10

so instead du/e^(6u)=e^(3t)(dt)

Answer 11

\[\frac{du}{dt}=e^{6u+3t}\]
\[\frac{du}{dt}=e^{6u}\ e^{3t}\]
\[\int\{\frac{du}{e^{6u}}=e^{3t}dt\}\]

Answer 12

so ln(abs(e^6u))=e^3t^2+c