6. Exercise 4. (Strauss, Exercise 1.2.6.) a) Solve the equation: $y u_x + x u_y = 0$, with the condition $u(0, y) = e^{-y^2}$. b) In which region of the xy-plane is the solution uniquely determined?
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We can rewrite this equation as: xu + yux = 0 Step 2: Use the product rule The equation xu + yux = 0 can be rewritten using the product rule as: (xu)y + (yux) = 0 Step 3: Simplify the equation Using the product rule, we can simplify the equation as: xyu + Show more…
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