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# 2.5 Notes - To Solve Substitute y=vx This substitution will...

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Slide 1 Solutions by Substitution Homogeneous and Bernoulli Equations Section 2.5 Slide 2 Homogeneous Functions Homogeneous Function of Degree n ) , ( ) , ( y x f t ty tx f n = Slide 3 Example Is homogeneous? 2 3 2 3 4 ) , ( xy x y x y x f + - =

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Slide 4 Homogeneous Differential Equation A homogeneous differential equation is an equation of the form where M and N are homogeneous functions of the same degree. 0 ) , ( ) , ( = + dy y x N dx y x M Slide 5 Example: Determine if the equations are homogeneous: ( 29 0 2 2 = + + dy y dx xy x ( 29 0 1 2 2 = + + dy y dx x Slide 6 Solving a Homogeneous Differential Equation
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Unformatted text preview: To Solve: Substitute y=vx. This substitution will transform the homogeneous differential equation into a separable equation. Slide 7 Bernoullis Equation The differential equation where n is any real number is called a Bernoullis equation . To solve, substitute n y x f y x P dx dy ) ( ) ( = + n y u-= 1 Slide 8 Examples y x y x y = + 1 x e y y y =- 2 2...
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