Question: Find the general solution of each PDE. The solution u is a function of the variables which appear, unless otherwise stated. 1. = 2x

Find the general solution of each PDE. The solution u is a

Find the general solution of each PDE. The solution u is a function of the variables which appear, unless otherwise stated. 1. = 2x 2. ur sin x + cos y 9. Uxyzz = 0 3. usin x + cosy, u = u(x, y, z) 4. Uyy = xy 5. Uxy = x - y 6. Uxxy 7. Uxxyy = 0 = sin 2x 8. Uxzz = xyz + y 10. Uxyyzzxyz 11. Uy u=0, u = u(x,y) - 12. ux+3u = e, u = u(x, y) 13. uyu 0 14. ux+3uxy + y = 15. uy+xu= 2 16. uzu=y-z 17. uxxux-2u = 0, u = u(x, y) 32

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