Chapter 16.4, Problem 19E

(a)

To determine

To calculate: The series solution of the differential equation $y^{″}-xy\text{'}=0$ that satisfies the initial conditions $y(0)=0,y^{\prime }(0)=2$ by using Taylor series.

(b)

To determine

To graph: Draw the graph of third degree and fifth degree series using graphical utility

(c)

To determine

Whether the solution $y=2x+\frac{1}{3}{x}^3+\frac{6}{20}{x}^5$ is symmetry or not.