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(*) Solve the following equations using the method of characteristics. In each case, if the Cauchy condition is not given, find the general solution. 1. tut + 3xux 3u, 2. aux + buy = 0, where a and b are two constants, 3. x³ux + yuy = 0, = 4. (**) x²ux + y² uy - 5. yur — xuy=U, 6. xux + yuy = ye²u, 7. (**) Uux + Uy = 1, (x + y)u,

(*) Solve the following equations using the method of characteristics. In each case, if the Cauchy condition is not given, find the general solution. 1. tut + 3xux 3u, 2. aux + buy = 0, where a and b are two constants, 3. x³ux + yuy = 0, = 4. (**) x²ux + y² uy - 5. yur — xuy=U, 6. xux + yuy = ye²u, 7. (**) Uux + Uy = 1, (x + y)u,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. (*) Solve the following equations using the method of characteristics. In each case, if the Cauchy condition is not given, find the general solution. 1. tut + 3xux = 3u, 2. aux + buy = 0, where a and b are two constants, 3. x³ux + yuy = 0, 4. (**) x²ux + y²uy = (x + y)u, 5. yux = xUy U₂ 6. xux + yuy = ye²u, 7. (**) uux + Uy = 1,
Transcribed Image Text:6. (*) Solve the following equations using the method of characteristics. In each case, if the Cauchy condition is not given, find the general solution. 1. tut + 3xux = 3u, 2. aux + buy = 0, where a and b are two constants, 3. x³ux + yuy = 0, 4. (**) x²ux + y²uy = (x + y)u, 5. yux = xUy U₂ 6. xux + yuy = ye²u, 7. (**) uux + Uy = 1,
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