Suppose that the following initial value problem has a power series solution of the form y = 2n=0 an x". y" + Sy(s) ds = x, y (0) = 0, y'(0) = 1 a) Find the recurrence relation satisfied by an . b) Determine the first five nonzero terms of the series E=0 an x". c) Solve the recurrence relation you find in part (a), i.e express an in terms of n. d) Show that solutions you find is converging.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.