Differential Equations Lecture Work Solutions 229

Differential Equations Lecture Work Solutions 229 - 3. uxx...

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3. u xx = au t + bu x b 2 4 u + d A =1 B = C =0 ⇒4 = 0 parabolic dx dt = 0 already in canonical form since u xx is the only 2 nd order term u = υe b 2 x u x = υ x e b 2 x + b 2 b 2 x u xx = υ xx e b 2 x + x e b 2 x + b 2 4 b 2 x u t = υ t e b 2 x υ xx + x + b 2 4 υ = t + b υ x + b 2 υ ! b 2 4 υ
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