74.17.1 problem 1

Internal problem ID [16532]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 09:10:18 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+6 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 32

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

\[ y = \sqrt {x}\, \left (c_{1} x^{-\frac {i \sqrt {23}}{2}}+c_{2} x^{\frac {i \sqrt {23}}{2}}\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 44

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

\[ y(x)\to c_1 x^{\frac {1}{2} \left (1+i \sqrt {23}\right )}+c_2 x^{\frac {1}{2} \left (1-i \sqrt {23}\right )} \]