A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
can some the heat the equation for me?
Ut=(c^2)Uxx
u(t,0)=0 u(t,pi)=(pi)cost
u(0,x)=x
I want to know the steps
anonymous
 5 years ago
can some the heat the equation for me? Ut=(c^2)Uxx u(t,0)=0 u(t,pi)=(pi)cost u(0,x)=x I want to know the steps

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is non homogenous so I think you use solve it as a steady state separation of variables?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i don't know how to do it with the cost

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think it can be done that way. So since it's non homogenous, assume u(x,t)= v(x) + w(x,t) Take the partials of your assumption so you can plug back into your pde. So plugging it back in, you get 1. dw/dt=K(v(x)'' + K(d2w/dx2). Now you plug in your boundary conditions from the question into your assumption. So 2. v(0)+w(0,t)=0, v(pi)+w(pi,t)=picost and 3. v(x)+ w(x,0)=x. Now let t> infinity, so all of w(x,t) and its derivatives of 0. Using this to simplify our newly attained equations, we learn that: 0=v''(x) and v(0)=0, v(pi)=picost. Integrate v'' twice to solve for v(x). v(x)=c1x+c2. Plug in v(0)=0, v(pi)=picost to solve for the constants. C2=0 and C1=cost. Now you have v(x). Now plug in the values for v(x) to simplify the 3 equations i labelled back there. You will get: 1. dw/dt=Kd2w/dx2, 2. w(0,t)=0, w(pi,t)=0 (the cost is gone because v(pi)=picost so subtracting from both sides you get w(pi,t)=0), w(x,0)=xxcost. With these new BC, the pde is now homongeous. Now you can solve this new pde as a normal separation of variables going through eigenfunctions etc. I think you can use this method, but I'm not 100% sure as I said before. This is the furtherest type of pde I know how to solve so yeah haha

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, the third equation, 3. w(x,0)=xxcost is the initial condition on the last part incase you had trouble reading.
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.