Differential Equations Lecture Work Solutions 3

Differential Equations Lecture Work Solutions 3 - 4 uxy uy...

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Unformatted text preview: 4. uxy + uy = 0 Let v = uy then the equation becomes vx + v = 0 For fixed y , this is a separable ODE dv = −dx v ln v = − x + C (y ) v = K (y ) e− x In terms of the original variable u we have uy = K (y ) e− x u = e− x q (y ) + p(x) You can check your answer by substituting this solution back in the PDE. 3 ...
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