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anonymous
 5 years ago
Find the solution to the differential equation, subject to the given initial condition 6*dp/dt=p^4, p(0)=9. it seems so simple but cant get the answer right
please Help!
anonymous
 5 years ago
Find the solution to the differential equation, subject to the given initial condition 6*dp/dt=p^4, p(0)=9. it seems so simple but cant get the answer right please Help!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is a separable differential equation. You just need to rearrange:\[6p^{4}dp=dt\]integrate and solve for your constant.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is this how you started?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Anyway, integrate both sides:\[6\frac{p^{3}}{3}=t+c \rightarrow 2p^{3}=t+c \rightarrow p^{3}=c\frac{t}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So\[p(0)=9 \rightarrow 9^{3}=c\frac{0}{2}=c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes and i have to write it out as p(t)= but i keep getting it wrong so far i havep^3=(t+C)/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I get\[p(t)=\sqrt[3]{\frac{2}{ct}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[p(0)=9 \rightarrow 9=\sqrt[3]{\frac{2}{c}} \rightarrow c=\frac{2}{9^3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yep thats what I've been plugging into wiley plus to no avail

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What exactly have you been plugging in?

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.0i get a constant of 2/243 > p(t) = cubed root (486/(243t  2))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cubed root of (2/729t)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Maybe you need to use \[c=\frac{2}{9^3}\]for a solution\[p(t)=\sqrt[3]{\frac{2}{t+c}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[p(t)=9\frac{\sqrt[3]{2}}{\sqrt[3]{9^3t2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0These are just different ways of saying the same thing. These online submission things are such a crapshoot.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i have new values now 3 *du/dt= u^3, u(0)=6 which then i get once integrated u^2= 2/3t+C

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0substituting gives me c=1/12 so u(t)=square root (2/3t+1/12)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you are correct a crapshoot it is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[u= \frac{6}{\sqrt{124t}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0positive root only satisfies the boundary condition.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0once you integrated did you get 3/2 u^2=t+C

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and this checks out with wolfram alpha

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{3}{2}u^{2}=t+c\]after integration.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0aha i see what you did, nice job! Thank you for the help!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, does that mean your other question is defunct now?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well i have an understanding of the problem but all of my attepmts are used
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