In 13–16 proceed as in Example 3 and obtain the first six

QUESTION:

In Problems 15–18 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.

\(y^{\prime \prime}=x^{2}+y^{2}-2 y^{\prime}, \quad y(0)=1, y^{\prime}(0)=1\)

Text Transcription:

y^prime\prime=x^2+y^2-2y^prime,y(0)=1,y^prime(0)=1