Chapter 6.1, Problem 32E

In Problems 31–34 verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x²ⁿ⁺¹ let k = n + 1.]

32. $y={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{(-1)}^n{x}^{2n}}$, (1 + x²)y′ + 2xy = 0