Differential Equations Lecture Work Solutions 82

Differential Equations Lecture Work Solutions 82 - d. u t +...

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15. a. u xx + u yy =1 Try u ( x, y )= X ( x ) Y ( y ) X 0 Y + XY 0 =1 This is NOT separable. But the homogeneous equation is. b. u xx + u yy = u Try u ( x, y )= X ( x ) Y ( y ) X 0 Y + XY 0 = XY Divide by XY X 0 X =1 Y 0 Y The equation is separable. c. x 2 yu xx + y 4 u yy =4 u Try u ( x, y )= X ( x ) Y ( y ) x 2 yX 0 Y + y 4 XY 0 =4 XY Divide by yXY x 2 X 0 X = 4 y y 3 Y 0 Y The equation is separable.
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Unformatted text preview: d. u t + uu x = 0 Try u ( x, t ) = X ( x ) T ( t ) TX + XX T 2 = 0 Divide by XT 2 T T 2 = X The equation is separable. 82...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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