Question: 3. Consider the PDE 2. - 1 = 4y a) Find the general solution in two different ways. Use two different coordinate transformations: one with

3. Consider the PDE 2. - 1 = 4y a) Find

3. Consider the PDE 2. - 1 = 4y a) Find the general solution in two different ways. Use two different coordinate transformations: one with z = x and one with z = y. b) Consider the side condition u(x, 0) = ex Find the particular solution of the PDE that satisfies the given side condition in two different ways, using both of the general solutions you found in part a). c) Are the two solutions you found in part b) the same? Would they be the same for any side condition that is valid? Explain why or why not

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