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Question

The degree of the homogeneous function x2sin(y2x2)+y2is ___

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Solution

So how to check the degree of a homogeneous function? We discussed that f(x,y) has to be written as f(kx,ky) first. So let’s do that.
f(x,y)=x2(sin(y2x2))+y2f(kx,ky)=k2x2(sin(k2y2k2x2))+k2y2=k2(x2sin(y2x2)+y2)
So we can notice that after multiplying each x and y with k we can rewrite the function in such a manner that we can take k2 out as common leaving every x and y independent of k.
Here k2 is common. Rest of the function is independent of k. Now degree of a homogeneous function is that power of k which was taken out as common factor. Here its k2. So degree of the given homogeneous function is 2.

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