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M1 differential equations of first order and first degree

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Differential EQUATIONS of the FIRST order and first degree. Any differential equation of the first order and first degree can be written in the form



Example. The differential equation


             


can also be written as


            (X - 3y)dx + (x - 2y)dy = 0

 


Existence of a solution. The general solution of the equation dy/dx = g(x, y), if it EXISTS, has the form f(x, y, C) = 0, where C is an arbitrary constant. Under what circumstances does a general solution exist? We have the following theorem.


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