numerical solver

numerical solver

In Problems 13–16 proceed as in Example 3 and obtain the first six nonzero terms of a Taylor series solution, centered at 0, of the given initial-value problem. Use a numerical solver and a graphing utility to compare the solution curve with the graph of the Taylor polynomial.
13. y” = x + y2, y(0) = 1, y'(0) = 1
14. y” + y2 = 1, y(0) = 2, y'(0) = 3
15. y” = x2 + y2 – 2y’, y(0) = 1, y'(0) = 1
16. y” = ey, y(0) = 0, y'(0) = – 1