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Homogeneous Differential Equation

Determine whe...

Question

Determine whether or not the following function is homogeneous: $f (x, y) = x sin y + y sin x$
If homogeneous enter 1 else enter 0.

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Solution

Consider, $f (x, y) = x s i n y + y s i n x$

$=\Rightarrow f (t x, t y) = t x s i n t y + t y s i n t x$

$= t (x s i n t y + y s i n t x)$

$=\neq t^{k} f (x, y)$
For any $k ϵ R$
Hence the answer is 0

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