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Question
Let u = x2y3 cos`(x/y)`. By using Euler’s theorem show that `x*(del"u")/(delx) + y * (del"u")/(dely)`
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Solution
Given, u = x2y3 cos`(x/y)`
i.e., u(tx, ty) = (tx)2 (ty)3 cos`("tx"/"ty")`
= t2x2t3y3 cos`(x/y)`
= t5x2y3 cos`(x/y)`
= t5 u
∴ u is a homogeneous function in x and y of degree 5.
∴ By Euler’s theorem, `x * (del"u")/(delx) + y * (del"u")/(dely)` = 5u
Hence Proved.
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