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Which one of the following function(s) is/are homogeneous? {({
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Which one of the following function(s) is/are homogeneous? \displaystyle{\left({a}\right)}{f{{\left({x},{y}\right)}}}=\frac{{{x}-{y}}}{{{x}^{{2}}+{y}^{{2}}}}{\left({b}\right)}{f{{\left({x},{y}\right)}}}={x}^{{\frac{{1}}{{3}}}}{y}^{{-\frac{{2}}{{3}}}}{{\tan}^{{-{{1}}}}{\left(\frac{{x}}{{y}}\right)}}{\left({c}\right)}{f{{\left({x},{y}\right)}}}={x}{\left({\ln{\sqrt{{{x}^{{2}}+{y}^{{2}}}}}}-{\ln{{y}}}\right)}+{y}{e}^{{\frac{{x}}{{y}}}} (d) none of these

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Which one of the following function(s) is/are homogeneous? \displaystyle{\left({a}\right)}{f{{\left({x},{y}\right)}}}=\frac{{{x}-{y}}}{{{x}^{{2}}+{y}^{{2}}}}{\left({b}\right)}{f{{\left({x},{y}\right)}}}={x}^{{\frac{{1}}{{3}}}}{y}^{{-\frac{{2}}{{3}}}}{{\tan}^{{-{{1}}}}{\left(\frac{{x}}{{y}}\right)}}{\left({c}\right)}{f{{\left({x},{y}\right)}}}={x}{\left({\ln{\sqrt{{{x}^{{2}}+{y}^{{2}}}}}}-{\ln{{y}}}\right)}+{y}{e}^{{\frac{{x}}{{y}}}} (d) none of these
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Which one of the following function(s) is/are homogeneous? \displaystyle{\left({a}\right)}{f{{\left({x},{y}\right)}}}=\frac{{{x}-{y}}}{{{x}^{{2}}+{y}^{{2}}}}{\left({b}\right)}{f{{\left({x},{y}\right)}}}={x}^{{\frac{{1}}{{3}}}}{y}^{{-\frac{{2}}{{3}}}}{{\tan}^{{-{{1}}}}{\left(\frac{{x}}{{y}}\right)}}{\left({c}\right)}{f{{\left({x},{y}\right)}}}={x}{\left({\ln{\sqrt{{{x}^{{2}}+{y}^{{2}}}}}}-{\ln{{y}}}\right)}+{y}{e}^{{\frac{{x}}{{y}}}} (d) none of these