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Exercise 103

Avg difficulty 2.5

Take ytt=100yxxy_{tt} = 100y_{xx}, 0<x<40 < x < 4, t>0t > 0, y(0,t)=y(4,t)=0y(0,t) = y(4, t) = 0, y(x,0)=F(x)y(x,0) = F(x), and yt(x,0)=0y_t(x,0) = 0. Suppose that F(0)=0F(0)=0, F(1)=2F(1)=2, F(2)=3F(2)=3, F(3)=1F(3)=1. Using the d'Alembert solution find

  1. y(1,1)y(1,1),
  2. y(4,3)y(4,3),
  3. y(3,9)y(3,9).

Lebl, Notes on Diffy Qs, §4.8 D'Alembert solution of the wave equation, exercise 103

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.