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Question
If V(x, y) = ex (x cosy – y siny), then Prove that `(del^2"V")/(delx^2) + (del^2"V")/(dely^2)` = 0
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Solution
V(x, y) = ex (x cosy – y siny)
`(del"V")/(delx)` = ex (x cosy – y siny) + ex cosy
`(del^2"V")/(delx^2)` = ex (x cosy – y siny) + ex cosy + ex cosy
`(del"V")/(dely)` = – xex (– siny) – ex (y cosy + siny)
`(del^2"V")/(dely^2)` = – xex cosy – ex (y(– siny) + cosy + cosy)
= – ex (x cosy – y siny) – 2ex cosy
`(del^2"V")/(delx^2) + (del^2"V")/(dely^2)` = ex [x cosy – y siny] + 2ex cosy
– ex (x cosy – y siny) – 2ex cosy
0
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