Question: Classify the following partial differential equation: (a) uxx + 4xy +Uyy+xux-yuy+2u = 0 (b) Uxx-2xUxy+Xuyy-yux-Uy+3u=0 (2) Verify that the indicated function is a solution

Classify the following partial differential equation: (a) uxx + 4xy +Uyy+xux-yuy+2u =

Classify the following partial differential equation: (a) uxx + 4xy +Uyy+xux-yuy+2u = 0 (b) Uxx-2xUxy+Xuyy-yux-Uy+3u=0 (2) Verify that the indicated function is a solution of the given PDE UUxx = 0; u(x,t)=e" (cos 3x-sin 3x) (3) Find the Product Solution of given PDE: (i) 3ux+2uy=0; u(x,0) = 4e *; (ii) 4ux+uy=3u; u(0,y)=e5y; (iii) Uxx=cUyy (4) Use D'Alembert's method to find the solution of wave equation du du 12 ????2' at i=0 = ; u(x,0)=cosx. = sinx

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