An ODE is said to be in quadrature format when the following conditions are met:

1) the ODE is of first order and the right hand sides below depend only on x or y(x):

quadrature_1_x_ode := diff(y(x),x)=F(x);

quadrature_1_y_ode := diff(y(x),x)=F(y(x));

2) the ODE is of high order and the right hand side depends only on x. For example:

quadrature_h_x_ode := diff(y(x),x,x,x,x)=F(x);

where F is an arbitrary function. These ODEs are just integrals in disguised format, and are solved mainly by integrating both sides.