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Exercise 103

Avg difficulty 2.5

Find the corresponding ODE problem for Y(x)Y(x), after transforming the tt variable ytt+3yxx+y=x+t,−1<x<1,t>0,y(−1,t)=0,y(1,t)=0,y(x,0)=(1−x2),yt(x,0)=0.\begin{aligned} & y_{tt} + 3y_{xx} + y = x+t, \qquad -1 < x < 1, \enspace t > 0, \\ & y(-1,t) = 0, \quad y(1,t) = 0, \quad y(x,0) = (1-x^2) , \quad y_t(x,0) = 0. \end{aligned} Do not solve the problem.

Lebl, Notes on Diffy Qs, §6.5 Solving PDEs with the Laplace transform, 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.