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Differential Equations Lecture Work Solutions 221

# Differential Equations Lecture Work Solutions 221 - 3 Show...

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6.6 General Solution Problems 1. Determine the general solution of a. u xx 1 c 2 u yy = 0 c = constant b. u xx 3 u xy + 2 u yy = 0 c. u xx + u xy = 0 d. u xx + 10 u xy + 9 u yy = y 2. Transform the following equations to U ξη = cU by introducing the new variables U = ue ( αξ + βη ) where α, β to be determined a. u xx u yy + 3 u x 2 u y + u = 0 b. 3 u xx + 7 u xy + 2 u yy + u y + u = 0 (Hint: First obtain a canonical form)
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Unformatted text preview: 3. Show that u xx = au t + bu x − b 2 4 u + d is parabolic for a , b , d constants. Show that the substitution u ( x, t ) = v ( x, t ) e b 2 x transforms the equation to v xx = av t + de − b 2 x 221...
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