nagle_differential_equations_ISM_Part56

nagle_differential_equations_ISM_Part56 - Exercises 8.6 18....

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Unformatted text preview: Exercises 8.6 18. 1 + x- 2 + 1 2 x- 2 2- 1 24 x- 2 4 + 22. a 1- x 2 2 + + x + x 2 2- x 3 6 + 24. a 1- 3 x 2 2 + + a 1 x- x 3 6 + + 2 3- x 2 26. a ( 1- x 2 ) + a 1 x- x 3 6 + + x 2 2 + 28. a 1 + x 3 6 + + a 1 ( x + ) + x 2 2 + 30. 1- t 2 2 + t 3 2- t 4 4 + EXERCISES 8.5: Cauchy-Euler (Equidimensional) Equations Revisited 2. c 1 x- 5 / 2 + c 2 x- 3 4. c 1 x- ( 1+ 13 ) / 2 + c 2 x- ( 1- 13 ) / 2 6. c 1 x cos ( 3 ln x ) + c 2 x sin ( 3 ln x ) 8. c 1 + c 2 x- 1 / 2 cos 5 2 ln x ! + c 3 x- 1 / 2 sin 5 2 ln x ! 10. c 1 x- 2 + c 2 x- 2 ln x + c 3 x- 2 (ln x ) 2 12. c 1 ( x + 2) 1 / 2 cos [ln( x + 2)] + c 2 ( x + 2) 1 / 2 sin [ln( x + 2)] 14. c 1 x + c 2 x- 1 / 2 + x ln x- 2 x- 2 ln x 16. 3 x- 2 + 13 x- 2 ln x EXERCISES 8.6: Method of Frobenius 2. 0 is regular 4. 0 is regular 6. 2 are regular 271 Chapter 8 8. 0, 1 are regular 10. 0, 1 are regular 12. r 2 + 3 r + 2 = 0; r 1 =- 1, r 2 =- 2 14. r 2- r = 0; r 1 = 1, r 2 = 0 16. r 2- 5 r 4- 3 4 = 0; r 1 = 5 + 73 8 , r 2 = 5- 73 8 18. r 2- r- 3 4 = 0; r 1 = 3 2 , r 2 =- 1 2 20. a 1- x 3- x 2 15- x 3 35 + 22. a 1 + 4 x + 4 x...
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nagle_differential_equations_ISM_Part56 - Exercises 8.6 18....

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