apply second bc uy 1 y e e g1 e g1 e y this

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Unformatted text preview: le, so the BVP has no solutions. This is impossible, so the BVP has no solutions. 2 xy 3 x2 5. (a) yuxx 4uxy + 2yuyy + exy ux x33u = xyexx22 5. (a) yuxx 4uxy + 2yuyy + exy ux x33u = xyex 22 xy x 5. (a) yuxx 4uxy + 2yuyy + exy u2x x3u = xyex 2 5. (a) yuxx 4uxy + 2yuyy + exy u2x x u = xyex 2 yy xx a =xx b = xy 4,, c = 2y ) b x 4ac = 16 8y 2.. a = y, b = xy 4 c = yyy ) b2 4ac = 16 8y 2 y, 2 2 a = y, b = 4,, c = 2y ) b2 4ac = 16 8y 2.. a = y, b = 4 c = 2y ) b2 4ac = 16 8y 2 2 Equation is hyperbolic if 16 8y 22 > 0 Equation is hyperbolic if 16 8y22 > 0 p p Equation is hyperbolic if 16 82y2 > 0 y Equation is hyperbolic if 16 82 > 0 Equation is parabolic if 16 8y 2 = 0 ) y = ± p2 Equation is parabolic if 16 8y 2 = 0 ) y = ± p2 Equation is parabolic if 16 28y 2 = 0 ) y = ± 2 Equation is parabolic if 16 8 y 2 = 0 ) y = ± 2 Equation is elliptic if 16 8y 22 < 0 Equation is elliptic if 16 8y22 < 0 Equation is elliptic if 16 8y 2 < 0 Equation is elliptic if 16 8y < 0 2 2 (b) 2uxx + cos(x)uxy + (1 sin22(x))uyy + cos22(x)u + sin(xy )ux (b) 2uxx + cos(x)uxy + (1 sin22(x))uyy + cos22(x)u + sin(xy )ux (b) 2uxx + cos(x)uxy + (1 sin2(x))uyy + cos2(x)u + sin(xy )ux (b) 2uxx + cos(x)uxy + (1 sin (2 ))uyy + cos (x)u + sin(xy )ux x yy xx xy yy x xx x a = 2,, b = cos(xxy,, c = (1 sin 22(x)) a = 2 b = cos(x) c = (1 sin2(x)) ) 2 2(x)) a = 2,, b = cos(x),, c = (1 sin (x)) a = 2 b = cos(x) 2 = (1 sin c 2 2 2 ) b22 4ac = cos22(x) 8(1 sin22(x)) = 7(sin22(x) 1). ) b22 4ac = cos22(x) 8(1 sin22(x)) = 7(sin22(x) 1). 2 2 )b ) b 4ac = cos (x) 8(1 sin2 (x)) = 7(sin2 (x) 1). 4ac = cos (x) 8(1 sin (x)) = 7(sin (x) 1). uy = tan(x) uy = tan(x) uy = tan(x) uy = tan(x) y y AMATH 350 AMATH 350 8. Solve the PDE Assignment #7 Solutions - Fall 2013 Page 8 Assignment #7 Solutions - Winter 2013 Page 7 2 u x + uy + u = 0 8. subject to the= 0; u(condition uxx, 0) = cos x. 2ux + uy + u initial x, 0) = cos ( . This is a first-order linear PDE, and we cannot solve it by pa...
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This note was uploaded on 02/08/2014 for the course AMATH 350 taught by Professor Davidhamsworth during the Fall '12 term at University of Waterloo, Waterloo.

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