A community for students.
Here's the question you clicked on:
 0 viewing
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!

This Question is Closed

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?

anonymous
 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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.