4.7 Notes - Slide 1 Cauchy-Euler Equations Differential...

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Slide 1 Cauchy-Euler Equations Differential Equations Section 4.7 Slide 2 Standard Form of a Cauchy- Euler Equation ) ( 0 1 2 2 ) 1 ( 1 1 ) ( x g y a y x a y x a y x a y x a n n n n n n = + + + + + - - - We will try to find a solution of the form m x y = Slide 3 Case I m 1 and m 2 are distinct real roots The solution has the form Example: #6 2 1 2 1 m m x c x c y + =
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Slide 4 Case II m 1 and m 2 are repeated real roots The solution looks like Example: #2 x x c x c y m m ln 1 1 2 1 + = Slide 5
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4.7 Notes - Slide 1 Cauchy-Euler Equations Differential...

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