# 5 Recall from \$18.3 Example 1 that the equation ²uzz - Ut = 0 ...

## Transcribed Text

5 Recall from \$18.3 Example 1 that the equation ²uzz - Ut = 0 with Dirichlet boundary conditions u(0,t) = u1 and u(L,t) = U2 for t > 0 has solutions of the form = + - n=1 with ln = nr/L for n = 1,2,3, Use this fact and techniques from \$18.3 to solve the equation Aurz - Ut = 0 for 0 < x < 5 and t > 0 with Dirichlet boundary conditions u (0,t) = 1 and u ( 5, t) = 9 for t > 0 and initial condition 1 + 5x, 0 < x < 2 = = 2 + 4x, 2 < x < 5

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