Use power series to solve the initial-value problem Answer: y = Σ 800 n=0 y" +3xy' +6y=0, y(0) = 0, y' (0) = 1. 0 x2n+ (-1)^n (3^n) (1/(2(n))) x2n+1 n=0

· Find a solution of the differential equation y'+ 5zy = 0 in the form of a power series in z. For a full credit, show every step clearly and write your final solution in summation notation involving the “E" sign. Start with y = E enz".

1 == using power series method. 1-X 4. y' - 2xy =

Use power series to solve the initial-value problem (x² – 2)/" + 10xy + 8y = 0 , y(0) = 1, y (0) = 0 . Answer: y = > 1 a2n +> x2n+1. n=0 n=0