Solving the Wave Equation PDE: A General Solution Approach

[sarahisme]

Hi everyone,

I'm having a bit of trouble with this pde problem:
http://img243.imageshack.us/img243/9313/picture3ui3.png

i get the answer to be u(x,t)=0 but i am guessing that's not right.

is the general solution to this problem: u(x,t) = f(x+ct) + g(x-ct) ??

thanks

sarah :)

 

[HallsofIvy]

No, it's not. That would be the general solution to the homogeneous wave equation, u_xx= c²u_tt, without a "source" term. Likewise, u(x,t)= 0 is the solution to the homogeneous equation with those conditions.

Remember that with a linear equation, you can construct a general solution to a non-homogeneous equation by adding the general solution to the related homogeneous equation to a single specific solution to the entire equation.

 

[sarahisme]

hmmm ok, i tried again and this is what i get...

for (a) http://img291.imageshack.us/img291/6120/picture4td7.png

for (b) http://img301.imageshack.us/img301/5572/picture5ii4.png

what do you think?

 

[sarahisme]

lol, well i think its right anyway, thanks for the help HallsofIvy! your a legend! :D