Question: Consider the PDE - xuyuy= 2u, for x > 0 and y> 0. Using the 3-step method of transformation reduce it to its canonical

Consider the PDE - xuyuy= 2u, for x > 0 and y>

Consider the PDE - xuyuy= 2u, for x > 0 and y> 0. Using the 3-step method of transformation reduce it to its canonical form, sketch its characteristic curves and obtain its general solution. [9 marks] ii) Find the specific solution of the PDE studied in i) when it is subject to the Cauchy data u(x, x) = 1/x, for x > 0. I (b) Use the method of characteristics to determine the solution of the different PDE TUYUy = u, - [2 marks] for x > 0 and y> 0 when it is subjected to the different Cauchy data u(x, x) = for x > 0. Hint: you may use the method of separation of variables to solve the nonlinear ODE that is the compatibility equation. [9 marks]

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