7/4/2015 Cauchy – Euler’s Equations Chapter 5 1

7/4/2015 Cauchy – Euler’s Equations Chapter 5 2

7/4/2015 Cauchy – Euler’s Equations Chapter 5 3

7/4/2015 Cauchy – Euler’s Equations Chapter 5 4 METHOD

7/4/2015 Cauchy – Euler’s Equations Chapter 5 5

7/4/2015 Cauchy – Euler’s Equations Chapter 5 6

7/4/2015 Cauchy – Euler’s Equations Chapter 5 7 Method for solving non – homogeneous Cauchy – Euler’s Equation

7/4/2015 Cauchy – Euler’s Equations Chapter 5 8

7/4/2015 Cauchy – Euler’s Equations Chapter 5 9

7/4/2015 Cauchy – Euler’s Equations Chapter 5 10

7/4/2015 Cauchy – Euler’s Equations Chapter 5 11

7/4/2015 Cauchy – Euler’s Equations Chapter 5 12

7/4/2015 Cauchy – Euler’s Equations Chapter 5 13

7/4/2015 Cauchy – Euler’s Equations Chapter 5 14 Solution:

7/4/2015 Cauchy – Euler’s Equations Chapter 5 15

7/4/2015 Cauchy – Euler’s Equations Chapter 5 16

7/4/2015 Cauchy – Euler’s Equations Chapter 5 17 Example:7.Solve the differential equation Solution:

7/4/2015 Cauchy – Euler’s Equations Chapter 5 18 Example:8. Solve the DE. Solution:Substitute

7/4/2015 Cauchy – Euler’s Equations Chapter 5 19

7/4/2015 Cauchy – Euler’s Equations Chapter 5 20

7/4/2015 Cauchy – Euler’s Equations Chapter 5 21

7/4/2015 Cauchy – Euler’s Equations Chapter 5 22

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

7/4/2015 Cauchy – Euler’s Equations Chapter 5 24

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 27