find the particular solution satisfying the given condition: \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{dy}\text{ }+\text{ }\left( \mathbf{x}\text{ }\mathbf{y}\text{ }+\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\mathbf{dx}\text{ }=\text{ }\mathbf{0};\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{1}\text{ }\mathbf{when}\text{ }\mathbf{x}\text{ }=\text{ }\mathbf{1}\]
find the particular solution satisfying the given condition: \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{dy}\text{ }+\text{ }\left( \mathbf{x}\text{ }\mathbf{y}\text{ }+\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\mathbf{dx}\text{ }=\text{ }\mathbf{0};\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{1}\text{ }\mathbf{when}\text{ }\mathbf{x}\text{ }=\text{ }\mathbf{1}\]