52.1.18 problem 16

Internal problem ID [8235]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 16
Date solved : Monday, January 27, 2025 at 03:46:36 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 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: 35

Order:=8; 
dsolve((x^2+1)*diff(y(x),x$2)-6*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 32

AsymptoticDSolveValue[(x^2+1)*D[y[x],{x,2}]-6*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_2 \left (x^3+x\right )+c_1 \left (-\frac {x^6}{5}+x^4+3 x^2+1\right ) \]