Differential Equations Lecture Work Solutions 211

Differential Equations Lecture Work Solutions 211 - To Find...

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To Find the general solution ! u ξη = 9 512 ( η ξ ) 3 64 u ξ = 9 512 ( 1 2 η 2 ηξ ) 3 64 η + f ( ξ ) u = 9 512 ( 1 2 η 2 ξ 1 2 ξ 2 η ) 3 64 ηξ + F ( ξ )+ G ( η ) = 9 512 · 1 2 ηξ ( ξ η ) 3 64 ηξ + F ( ξ )+ G ( η ) u ( x, y )= 9 1024 y 1 3 x ± ( y 3 x ) 1 3 x 3 x ± | {z } 8 3 x 3 64 y 1 3 x ± ( y 3 x ) + F ( y 3 x )+ G ( y 1 3 x ) = 9 1024 · 8 3 x y 1 3 x ± ( y 3 x ) 3 64 y 1 3 x ± ( y 3 x )+ F ( y 3 x ) + G ( y 1 3 x ) u ( x, y )= 3 128 x 3 64 ± ( y 1 3 x )( y 3 x )+ F ( y 3 x )+ G y 1 3 x ± check ! u x = 3 128 ( y 1 3 x )( y 3 x )+ ( 3 128 x 3 64 )( 1 3 )( y 3 x ) + 3 128 x 3 64 ± y 1 3 x ± ( 3) 3 F 0 ( y 3 x ) 1 3 G 0 y 1 3 x ± u y = 3 128 x 3 64 ± ( y 3 x )+ 3 128 x 3 64 ± y 1 3 x ± + F 0 ( y 3 x )+ G 0 y 1 3 x ± u xx = 3 128 1 3 ± ( y 3 x )+ 9
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