Differential Equations Lecture Work Solutions 269

Differential Equations Lecture Work Solutions 269 - 4....

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4. Solve u t +4 uu x =0 u ( x, 0) = 2 x< 1 3 x> 1 du dt u ( x, t )= u ( x 0 , 0) dx dt =4 u u ( x 0 , 0) dx u ( x 0 , 0) dt x u ( x 0 , 0) t + x 0 For x 0 < 1 x =8 t + x 0 x 8 t< 1 x 0 > 1 x =12 t + x 0 x 12 t> 1 u ( x, t 2 8 t 1 ?8 t 1 <x< 12 t 1
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