Classification pt 2

Classification pt 2 - University of Waterloo CivE 331...

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University of Waterloo CivE 331 Classify the following linear 2 nd order PDEs. Differential Equation Order Inde- pendent variables De- pendent variables Homogeneous or non- homogenous Parabolic, hyperbolic, or elliptic (a) ( 29 t u e u xx t tt sin + = - (b) 0 2 = + yy xx u y u (c) y xx t u u u + = 4 (d) C C C C x t xx 3 10 2 + + = (e) 0 = + yy xx u yu (f) ( 29 y x x t yy sin 3 = - (g) u u u u x xx t + + = 2 (h) ( 29 x u u u yy xy xx sin 3 = + + (i) ( 29 x u x u tt xx sin 2 + = (j) 0 = + + zz yy xx T T T
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University of Waterloo CivE 331 Classify the following linear 2 nd order PDEs (solutions). Differential Equation Order Inde- pendent variables De- pendent variables Homogeneous or non- homogenous Parabolic, hyperbolic, or elliptic (a) ( 29 t u e u xx t tt sin + = - 2 nd , non-homogeneous hyperbolic (b) 0 2 = + yy xx u y u 2 nd , homogeneous elliptic (c) y xx t u u u + = 4 2 nd 1 st – y, t , , homogeneous parabolic (d) C C C C x t xx 3 10 2 + + = 2 nd 1 st – t , homogeneous parabolic (e)
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Classification pt 2 - University of Waterloo CivE 331...

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