In Problems 7-18 find two power series solutions of the given differential equation about the ordinary...

 

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In Problems 7-18 find two power series solutions of the given differential equation about the ordinary point x = 0. 7. y + xy = 0 8. y + xy = 0 9. y" - 2xy + y=0 11. y + xy + xy = 0 10. y - xy + 2y = 0 12. " + 2xy + 2y = 0 13. (x-1)y"+y=0 14. (x + 2)y" + xy' - y = 0 15. "-(x+1)y'-y=0 16. (x²+1)y" - 6y=0 17. (x² + 2)y" + 3xy' - y = 0 18. (x² - 1)y" + xy' - y = 0 In Problems 7-18 find two power series solutions of the given differential equation about the ordinary point x = 0. 7. y + xy = 0 8. y + xy = 0 9. y" - 2xy + y=0 11. y + xy + xy = 0 10. y - xy + 2y = 0 12. " + 2xy + 2y = 0 13. (x-1)y"+y=0 14. (x + 2)y" + xy' - y = 0 15. "-(x+1)y'-y=0 16. (x²+1)y" - 6y=0 17. (x² + 2)y" + 3xy' - y = 0 18. (x² - 1)y" + xy' - y = 0