Question Find all the critical points of the nonlinear system dx dt = x y x 2 xy dy dt = x 2 y and identify their types The sketch a possible phaseportrait for the system Solution To find the critical points we need to find all solutions to the simulatanous equations x y x2 xy = 0 x2 y = 0 In general there is no guaranteed method for doing this, so be creative!List of nonlinear ordinary differential equations Jump to navigation Jump to search See also List of nonlinear partial differential equations A–F Name Order Equation Applications Abel's differential equation of the first kind 1 = Mathematics Abel's differential equation of the second kind Algebraically, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant Nonlinear functions are all other functions An example of a
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