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Show that the function $v = e^x (xsiny + ycosy)$ satisfies Laplace equation. Find its corresponding analytic function & its harmonic conjugate.
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written 7.9 years ago by
teamques10
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Given imaginary part $v = e^x (xsiny + ycosy)$
$\therefore v_{x} = \frac{\partial V}{\partial x} = e^x (sin y) + (xsin y + ycosy)e^x \\ \therefore v^{2}_{x} = \frac{\partial^2 V}{\partial x^2} = e^x (sin y) + e^x (sin y) + (xsiny + ycosy)e^x \\ v^{2}_{x} = e^x (-xsiny + y(-cosy) …
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