The radius of convergence of the power series solution of $y ^ { \prime \prime } - y = 0$ about $x = 0$ is
A) 0
B) 1
C) 2
D) $\infty$
E) none of the above

Question

Quizplus · Accepted Answer

The differential equation $y'' - y = 0$ is a linear homogeneous differential equation with constant coefficients. The power series solution of such an equation about any point (in this case, $x = 0$) typically has an infinite radius of convergence unless the equation has singular points, which this equation does not. Therefore, the radius of convergence of the power series solution is $\infty$.

The Radius of Convergence of the Power Series Solution Of y