45.1.14 problem 26

Internal problem ID [7214]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page 230
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:48:17 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: 30

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 25

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

\[ y(x)\to c_2 \left (x^3+x\right )+c_1 \left (x^4+3 x^2+1\right ) \]