A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."
anonymous
 one year ago
Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."

This Question is Closed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: two quantities, say A and B are inversely proportional if the subsequent condition olds: A*B = k where k is a constant

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2no, since that formula expresses the direct proportionality

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: we can write this: A= dy/dx, and B=y^4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay and now int(dy y^4) = int(dx k) (y^5)/5 = (x^2)/2 + C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y = \sqrt[5]{\frac{ 5x^2 }{ 2 } + C}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2I got this: \[\Large \begin{gathered} \int {{y^4}dy} = \int {kdx} \hfill \\ \hfill \\ \frac{{{y^5}}}{5} = kx + C \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0doesn't the right side turn into \[\frac{ kx^2 }{ 2 } + C\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no wait i see what i did wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so then \[y = \sqrt[5]{5kx + C}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2sorry! I had to specify this: \[\Large C \in \mathbb{R}\] since you are searching for a real funtion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0quick question what does the \[\epsilon \] mean

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2in general, in mathematical analysis, the mathematicians use \epsilon in order to indicate a small and positive quantity, which, in some case goes to zero

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay , double thank you :D
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.