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MATHS 361:  Partial Differential Equation

Tutorial 6:  Laplace transforms

1. Use laplace transforms to solve the ordinary differential equation:

uxx − 2ux − u = 0

ux (0) = 2,u(0) = 0

2.  Suppose you were instead given the boundary conditions u北 (1) = 0,u(1) = 2. How would you modify your approach? Would it still be possible to use the Laplace transform?

3. What about the boundary conditions u北 (0) = 0,u(1) = 2. Does this work, or does this cause problems. Why?

4. Use Laplace transforms to solve the partial differential equation:

2ut + ux = u,

u(x,0) = ex ,u(0,t) = t.

5. What if we instead had 2ut − u北 = 0? Would this equation work, or would it cause problems? Why?