anonymous
  • anonymous
hi i need help with differentiation equation
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
post yur question
anonymous
  • anonymous
Solve the seperable differential equation for u
anonymous
  • anonymous
du/dt =e^(4u-16t)

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anonymous
  • anonymous
Use the following initial condition: u(0) = 0 U = ?
anonymous
  • anonymous
u*
anonymous
  • anonymous
first lets re-write the equation:\[e^{4u-16t} = e^{4u}*e^{-16t} = {e^{4u} \over e^{-16t}} \]
anonymous
  • anonymous
can you solve from there?
anonymous
  • anonymous
this is calculus btw
anonymous
  • anonymous
ops typo, the last one should be => e^(16t) no negative cause it is as a fraction form
anonymous
  • anonymous
i did do that wat u rewritten
anonymous
  • anonymous
\[{du \over dt} = {e^{4u} \over e^{16t} } \]
anonymous
  • anonymous
is this calculus 1 ?
anonymous
  • anonymous
calculus 2 and i did do e^4u/e^16t how to proceed ?
anonymous
  • anonymous
e(-4u)du=e(-16t)dt solve it for each variable: (-1/4)* e(-4u)=(-1/16)*e^(-16t) + cont simplify
anonymous
  • anonymous
i found the constant to be -3/16
anonymous
  • anonymous
good?
anonymous
  • anonymous
ok. So, now all we do is separate 't' terms and 'u' tems\[{1\over e^{4u}} du= {1 \over e^{16t}}dt\]
anonymous
  • anonymous
yes but i found constant to be -3/16.... what to do next to find u?
anonymous
  • anonymous
is that constant correct?
anonymous
  • anonymous
mathmind, what happens to (-1/4) & (-1/16) coefficients (you have to get it after integration)
anonymous
  • anonymous
thats wat u get when u substitute both u and t with 0
anonymous
  • anonymous
initial condition u(o)=0, what about condition for t?
anonymous
  • anonymous
wasnt mentioned in my question
anonymous
  • anonymous
i found c = 0
anonymous
  • anonymous
agree with MathMind.. c=0
anonymous
  • anonymous
c = 0 u = 4t
anonymous
  • anonymous
is that answer?
anonymous
  • anonymous
yup
anonymous
  • anonymous
it doesnt work, my homework dont accept that
anonymous
  • anonymous
(-1/4)e^(-4u)=(-1/16)e^(-16t) +C -4u=C*(-16t) if u(0)=0, co C=0
anonymous
  • anonymous
HINT: To determine the constant of integration after you integrated both sides, DO NOT take natural logs, but rather just set u = 0 and t = 0 with u and t both still in the exponents. After determining the constant, then you need to take logs on both sides to solve for u. This is what the hint that my questioned offered.
anonymous
  • anonymous
same thing.. c will be equal 0.. that's just a shortcut.. kinda
anonymous
  • anonymous
you didn't tell this before... if u=0 & t=0 C=-1/4 +1/16 = -3/16
anonymous
  • anonymous
'oh wait nvm.. inik is right
anonymous
  • anonymous
so C is not zero? inik do u agree with mathmind?
anonymous
  • anonymous
can u figure out the u now?
anonymous
  • anonymous
comes from: (-1/4)e^(-4u)=(-1/16)e^(-16t) +C (-1/4)*1= (-1/16)*1 +C we did it!
anonymous
  • anonymous
so u = ?
anonymous
  • anonymous
just put value of C=-3/16 in: (-1/4)e^(-4u)=(-1/16)e^(-16t) +C simplify & take ln to both sides
anonymous
  • anonymous
I'm doing it now...
anonymous
  • anonymous
how do i take log of both sides am not good with logs
anonymous
  • anonymous
that is where i am confused at
anonymous
  • anonymous
give me sec
anonymous
  • anonymous
ok
anonymous
  • anonymous
you take ln to take away the e^\[\ln (e^x) = x\]
anonymous
  • anonymous
it only takes away e^?
anonymous
  • anonymous
wat if it is -e^
anonymous
  • anonymous
\[{-1 \over 4} e^{-4u}={-1 \over 16}e^{-16t} +C\] taking the Ln of everything so we can solve for u:\[{-1 \over 4}\ln (e^{-4u}) = {-1 \over 16} \ln(e^{-16t}) + \ln C\]\[{-1\over4} (-4u) = {-1 \over 16} (-16t) + \ln C\]
anonymous
  • anonymous
now do i plug in 0 for t?
anonymous
  • anonymous
let's try: e^(-4u)=1/4 * e^(-16t) +3/4 -4u=ln[1/4*(e^(-16t) +3)] u=-1/4 *[ln(e^(-16t)+3) - ln4] u=ln4/4 -1/4* ln(e^(-16t) +3)
anonymous
  • anonymous
t= variable unless you been asked to put t=o, you can't
anonymous
  • anonymous
u(t)=... u(0) = 0
anonymous
  • anonymous
not for general solution
anonymous
  • anonymous
what you mean?
anonymous
  • anonymous
it was not for you... sorry. you posted your response the same time as me...
anonymous
  • anonymous
oh haha alriught
anonymous
  • anonymous
I mean that the answer should be in form u(t)=...one thing if u(o) means t=0 - another. your response would be correct :)
anonymous
  • anonymous
have to go. Thank you MathMind & jophil - was fun!
anonymous
  • anonymous
np :D thanks for joining
anonymous
  • anonymous
i have to go now baii
anonymous
  • anonymous
ty to u 2 mathmind cya

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