9.7.13 problem problem 13

Internal problem ID [1054]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 13
Date solved : Monday, January 27, 2025 at 04:32:36 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

Order:=6; 
dsolve(diff(y(x),x$2)+9*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {9}{2} x^{2}+\frac {27}{8} x^{4}\right ) y \left (0\right )+\left (x -\frac {3}{2} x^{3}+\frac {27}{40} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

AsymptoticDSolveValue[D[y[x],{x,2}]+9*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {27 x^5}{40}-\frac {3 x^3}{2}+x\right )+c_1 \left (\frac {27 x^4}{8}-\frac {9 x^2}{2}+1\right ) \]