show that the given differential equation is homogeneous and solve each of them. \[~\left( {{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{x}\text{ }\mathbf{y} \right)\text{ }\mathbf{dy}\text{ }=\text{ }\left( {{\mathbf{x}}^{\mathbf{2}}}~+\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\text{ }\mathbf{dx}\]
show that the given differential equation is homogeneous and solve each of them. \[~\left( {{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{x}\text{ }\mathbf{y} \right)\text{ }\mathbf{dy}\text{ }=\text{ }\left( {{\mathbf{x}}^{\mathbf{2}}}~+\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\text{ }\mathbf{dx}\]