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[Solution] Consider the Cauchy problem x^2 u_x-x y u_y=u^2 subject to u=1, on x=y^2 ≠q 0 . Sketch the characteristics in the x-y plane. Describe the

Question: Consider the Cauchy problem

\[x^{2} u_{x}-x y u_{y}=u^{2}\]

subject to \(u=1\), on \(x=y^{2} \neq 0 .\)

  1. Sketch the characteristics in the \(x-y\) plane.
  2. Describe the set in the \(x-y\) plane where the solution is defined; i.e. those points which can be reached from the initial curve by following characteristics.
  3. Solve for \(u(x, y)\).
  4. Demonstrate that your solution satisfies the problem.

Price: $2.99
Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


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