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BERNOULLI�s DIFFERENTIAL EQUATIONS - Copy (2)

BERNOULLI�s DIFFERENTIAL EQUATIONS - Copy (2) - A...

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A. Alaca MATH 1005 Winter 2010 2 BERNOULLI’s DIFFERENTIAL EQUATIONS Definition: An equation of the form y + P ( x ) y = Q ( x ) y n , where n is any real number is called Bernouli’s equation. Note: When n = 0, we have a first order lin. diff. eqn. If n = 1 (and y = 0), then y y + P ( x ) = Q ( x ) y y = Q ( x ) - P ( x ) d dx (ln y ) = Q ( x ) - P ( x ) ln y = ( Q ( x ) - P ( x )) dx Let n = 0 , 1. Then the substitution u = y 1 - n transforms Bernoulli’s equation into a first order linear equation.
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