For (10), X can be omitted. Let y'=P, the equation becomes DP/(P 3+P) = dx, which is (2/P-2p/( 1+P 2) DP = 2dx (both sides are multiplied by 2) after integration.
equation of motion
The algebraic equation describing the relationship between variables under static conditions-the derivatives of variables are zero-is called static mathematical model; Differential equations describing the relationship between the derivatives of variables are called dynamic mathematical models, and these equations are motion equations.
The order of the equation of motion refers to the order of the highest derivative in the equation of motion. For example, the equation of motion of order n means that the highest derivative in the equation is order n..