verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y = Ax : xy′ = y (x ≠ 0)

Differentiating both sides with respect to x, we get,

y’ = A

Substituting the values of y’ in the given differential equations, we get,

\[\begin{array}{*{35}{l}}

=\text{ }xy  \\

=\text{ }x\text{ }\times \text{ }A  \\

=\text{ }Ax  \\

=\text{ }Y\text{ }\ldots   \\

\end{array}\]

= RHS

Therefore, the given function is a solution of the given differential equation