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Homework Help: Heat equation and Wave equation problems

  1. Oct 25, 2012 #1
    Solve the Heat equation u_t = ku_xx for 0 < x < ∏, t > 0 with the initial condition

    u(x, 0) = 1 + 2sinx

    and the boundary conditions u(0, t) = u(∏, t) = 1

    (Notice that the boundary condition is not homogeneous)

    Find the solution of the Wave equation u_tt = 4 u_xx with

    u(0, t) = u (π/2, t) = 0, t > 0

    u(x, 0) = sin (2x) - 2sin(6x), u_x (x, 0) = -3 sin4x, 0 ≤ x ≤ ∏/2

    Please help!! =[....
  2. jcsd
  3. Oct 26, 2012 #2


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    welcome to pf!

    hi dominic.tsy! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)

    show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
  4. Oct 26, 2012 #3


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    Define v(x, t)= u(x,t)- 1. What differential equation, boundary condition, and initial condition does that satisfy?

    Try a Fourier series solution of the form [tex]\sum A_n(t) sin(nx/4)+ B)n(t)cos(nx/4)[/tex]
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