Example 2-2 Find the general solution of the linear PDE 6 xu$_x$ - yu$_y$ + y$^2$u = y$^2$ First Step: Find the characteristics Second Step: Reduce the PDE Third Step: Solve the PDE a) Homogeneous solution b) Particular solution c) General solution
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Q. (a) Find a general solution to the PDE uxy = 0. (Give your answer in terms of two arbitrary functions.) (b) Solve the nonlinear PDE in the function u : R^2 → R: (∆u)^2 - 2uxx uyy = 0. Give your answer as general as possible, and note that this solution does not contain arbitrary functions (though it will have arbitrary coefficients). What is the key difference between this PDE and that in part (a)?
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