Number 15 pratice problems ### Chapter 6: Series Solutions of Linear Equations#### 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. \( y'' - 2xy' + y = 0 \)10. \( y'' xy' + 2y = 0 \)11. \( y'' + x^2y' + xy = 0 \)12. \( y'' + 2xy' + 2y = 0 \)13. \( (x - 1)y'' + y' = 0 \)14. \( (x + 2)y'' + xy' - y = 0 \)15. \( (x - 1)y'' + 2xy' - y = 0 \)16. \( (x - 2)y'' - 6y = 0 \)17. \( (x^2 + 2)y'' + 3xy' - y = 0 \)18. \( (x^2 - 1)y'' + xy' - y = 0 \)#### In Problems 19–22, use the power series method to solve the given initial-value problem.19. \( (x - 1)y'' - xy' + y = 0 \), \( y(0) = 2 \), \( y'(0) = 6 \)20. \( (x + 1)y'' -(2 - x)y' + y = 0 \), \( y(0) = 2 \), \( y'(0) = -1 \)21. \( y'' - 2xy'' + 8y = 0 \), \( y(0) = 3 \), \( y'(0) = 0 \)22. \( (x - 1)y'' + 2xy' = 0 \), \( y(0) = 0 \), \( y'(0) = 1 \)#### In Problems 23 and 24, use the procedure in Example 8 to find two power series solutions of the given differential equation about the ordinary point \( x = 0 \).*Note: Example 8 from the referenced textbook is not provided here.*#### Computer Lab

Name: Number 15 pratice problems ### Chapter 6: Series Solutions of Linear E
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Description: Number 15 pratice problems ### Chapter 6: Series Solutions of Linear Equations#### 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.