..(ii)
= 
L.H.S. of eq. (ii) = 
R.H.S. of eq. (ii) = 
= 
[From eq. (i)]
= 
= 
= 
= 
= 
L.H.S. = R.H.S
Hence, 
given by eq. (i) is a solution of .
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[\mathbf{y}\text{ }=\text{ }\mathbf{x}\text{ }\mathbf{sinx}\text{ }:\text{ }\mathbf{xy}\text{ }=\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{x}\text{ }(\surd ({{\mathbf{x}}^{\mathbf{2}}}~-\text{ }{{\mathbf{y}}^{\mathbf{2}}}))\text{ }\left( \mathbf{x}\text{ }\ne \text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{x}>\mathbf{y}\text{ }\mathbf{or}\text{ }\mathbf{x}<\text{ }\text{ }-\mathbf{y} \right)\]
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[\mathbf{y}\text{ }=\text{ }\mathbf{x}\text{ }\mathbf{sinx}\text{ }:\text{ }\mathbf{xy}\text{ }=\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{x}\text{ }(\surd ({{\mathbf{x}}^{\mathbf{2}}}~-\text{ }{{\mathbf{y}}^{\mathbf{2}}}))\text{ }\left( \mathbf{x}\text{ }\ne \text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{x}>\mathbf{y}\text{ }\mathbf{or}\text{ }\mathbf{x}<\text{ }\text{ }-\mathbf{y} \right)\]