First Order Equations of Second Degree

The order of a differential equation corresponds to the highest derivative, whereas the degree is associated with the power to which the highest derivative is raised. 

A nonlinear equation, which is first order and second degree, is 

This requires a different approach, as nonlinear systems often do. The first step is to replace p = dy/dx and solve the remaining quadratic equation for p 

We observe two branches are possible, depending on selection of sign. The appearance of the linear difference (jc — y) suggests replacing = jc — y, so 

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