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IntroFirstOrderODE

# IntroFirstOrderODE - we rewrite the equation in...

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First Order Ordinary Differential Equations The first order O.D.E. to be studied in this chapter may be expressed in either 1) derivative form dy dx = f(x,y) 2) differential form M(x,y) dx + N(x,y) dy = 0 Remark : An equation in one of these forms may easily be written in the other form. Examples : 1) Given the equation in derivative form dy dx = ! 2y x , where x is the independent variable and y is the dependent variable,
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Unformatted text preview: we rewrite the equation in differential form as 2y dx + x dy = 0 where M(x,y) = 2y and N(x,y) = x 2) Given the equation in differential form dx 1 + x 2 + dy 1 + y 2 = 0 where M(x,y) = 1 1 + x 2 and N(x,y) = 1 1 + y 2 we rewrite the equation in derivative form as dy dx = ! 1 + y 2 1 + x 2...
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