What is the solution of y' equals xy in differential equations?

The differential equation ( y' = xy ) can be solved using the method of separation of variables. Rearranging gives ( \frac{dy}{y} = x , dx ). Integrating both sides yields ( \ln|y| = \frac{x^2}{2} + C ), where ( C ) is the constant of integration. Exponentiating results in the general solution ( y = Ce^{\frac{x^2}{2}} ).