Question

find u(x,t) corresponding to the initial values f(x)=sinx,g(x)=0,when u(0,t)=0 du/dx(pi/2,t)=0,c=1

Answer 1

May I help?

Answer 2

yes please

Answer 3

Thank you.

Answer 4

Can you type it in clearly in Equation box?

Answer 5

find u(x,t) corresponding to the initial values f(x) = sin x, g(x)=0, when u(0,t)=0, (αu/αx) (π/2),t)=0, c=1
the wave equation u=1/2(f(x+ct)+f(x-ct)) and since g(x)=0 so we don't need to consider it.

Answer 6

\[U=1/2f((x+ct)+(x-ct))+c/2\int\limits_{x-ct}^{x+ct}g(x)dx\]

Answer 7

grade #? if I may know

Answer 8

sure

Answer 9

http://www.integral-calculator.com/
Hope that helps

Answer 10

Confirm: the wave equation is
\[U=\dfrac{ f(x+ct) + f(x-ct)}{2} \]
or \(U =\dfrac{1}{2(f(x+ct)+f(x-ct))}\)

One more thing: \(U'_x(\pi/2,t) =0\) and \(c =1\)

Question: \(c=1\) is for \(U'_x\) only or for the original U(x,t)?

Answer 11

welcome to os