9. Show that the following functions satisfy the equation Urr +Uyy = 0, known as the two-dimensional Laplace equation: (a) u(x,y) = x² − y² − 3xy + 5x − 6 (b) u(x, y) = ln(x² + y²), (x,y) ‡ (0,0) (c) u(x, y) = eª sin y. 10. Show that the following functions satisfy the equation Utt = Uxx + Uyy, known as the two-space-dimensional wave equation: (a) u(x, y, t) = e¹-t — 3e³+¹ +7xy - t + 13 (b) u(x, y, t) = (3x − 4y + 5t)ª, a a constant.

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A: Write -6-19x-11x2 in the linear combination of -1-x-x2, 1+2x+x2 and -1-3x-2x2.