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7/4/2015 Cauchy – Euler’s Equations Chapter 5 1
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 2
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 3
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 4 METHOD
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 5
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 6
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 7 Method for solving non – homogeneous Cauchy – Euler’s Equation
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 8
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 9
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 10
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 11
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 12
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 13
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 14 Solution:
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 15
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 16
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 17 Example:7.Solve the differential equation Solution:
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 18 Example:8. Solve the DE. Solution:Substitute
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 19
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 20
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 21
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 22
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 23 Method II Cauchy-Euler equation can be transformed to DE with constant coefficients by using transformation
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 24
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 25 Example:9. Solve the Cauchy- Euler equation by transforming it into a differential equation with constant coefficients. Solution:
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 26
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7/4/2015 Cauchy – Euler’s Equations Chapter 5 27
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