Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
windsylph
Group Title
PDE's: For the partial differential equation u_tt = 9u_xx, a general solution is u(x,t) = F(x+3t)+G(x3t). Find a particular solution with initial conditions u(x,0)=0, u_t(x,0)=sin(pi*x), u(0,t)=u(1,t)=0.
 2 years ago
 2 years ago
windsylph Group Title
PDE's: For the partial differential equation u_tt = 9u_xx, a general solution is u(x,t) = F(x+3t)+G(x3t). Find a particular solution with initial conditions u(x,0)=0, u_t(x,0)=sin(pi*x), u(0,t)=u(1,t)=0.
 2 years ago
 2 years ago

This Question is Closed

windsylph Group TitleBest ResponseYou've already chosen the best response.1
I'm having trouble especially using/interpreting the last initial condition.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
before we look at initial conditions do you know how to do this part: solve for particular solution \[u_{t t}=9u_{xx}\] ? is it separation of variables?
 2 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.1
If the problem asked me to solve it, yeah I would use separation of variables since that's the only method I know so far. but the problem only stated that the given solution is indeed a solution. actually, the first part of this problem was to show that the given solution is indeed a solution, the second part is this.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
\[u(x,0)=F(x+3(0))+G(x3(0))=F(x)+G(x)=0\] f(x)+g(x)=0 \[u_t=3f(x+3t)3g(x3t)\] \[u_t(x,0)=3f(x)3g(x)=\sin(\pi x)\] \[u(0,t)=u(1,t)=0\] \[u(0,t)=F(0+3t)+G(03t)=F(3t)+G(3t)=0\] \[u(1,t)=F(1+3t)+G(13t)=0\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
so we have \[F(x)+G(x)=0\] \[f(x)+g(x)=0\] \[3f(x)3g(x)=\sin(\pi x)\] \[F(3t)+G(3t)=0\] \[F(1+3t)+G(13t)=0\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
\[f(x)+g(x)=0 => f(x)=g(x) =>3f(x)+3f(x)=\sin(\pi x)\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
\[f(x)=\frac{1}{6} \sin(\pi x)\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
F(x)=\[\int\limits_{}^{}f dx=\int\limits_{}^{}\frac{1}{6} \sin(\pi x) dx=\frac{1}{6} \cos(\pi x) +c_1\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
\[3f(3t)3g(3t)=0 => f(3t)g(3t)=0 => f(3t)=g(3t)\] \[3f(1+3t)3g(13t)=0 => f(1+3t)=g(13t)\] i hope some of this will help i have to leave
 2 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.1
thanks still! ill look at it
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.0
you might want to check what i wrote for mistakes gl
 2 years ago
See more questions >>>
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.