19.18. Show that each of the following functions call each one u(x, y)- is harmonic, and find the function's harmonic partner, v(x, y), such that u(x, y) + iv(x, y) is analytic. Hint: Use C-R...

Extracted text: 19.18. Show that each of the following functions call each one u(x, y)- is harmonic, and find the function's harmonic partner, v(x, y), such that u(x, y) + iv(x, y) is analytic. Hint: Use C-R conditions. (a) a³ – 3ry?. (b) е" cos y. (c) x2 + y? where x2 + y? 0. -2y (d) е cos 2x. (e) ey²-x² cos 2xy. (f) e" (x cos y – y sin y) + 2 sinh y sin x + x° – 3xy² + y.