Consider the general first order Linear Ordinary Differential Equation: $$ \frac{dy}{dx} = A(x,y) = \frac{F(x,y)}{G(x,y)}$$
This equation is characteristic equation of the Partial Differential Equation:
$$G(x,y) \frac{\partial z}{\partial x} + F(x,y) \frac{\partial z}{\partial y} = 0 $$
Then is it true that a general solution to the partial differential equation above, means we have a solution to every possible ODE of the form:
$$ \frac{dy}{dx} = A(x,y) $$