18.3.10 problem Problem 16.12 (a)

Internal problem ID [3510]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 16, Series solutions of ODEs. Section 16.6 Exercises, page 550
Problem number : Problem 16.12 (a)
Date solved : Monday, January 27, 2025 at 07:40:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

Order:=6; 
dsolve((z^2+5*z+6)*diff(y(z),z$2)+2*y(z)=0,y(z),type='series',z=0);
 

\[ y \left (z \right ) = \left (1-\frac {1}{6} z^{2}+\frac {5}{108} z^{3}-\frac {13}{1296} z^{4}+\frac {5}{2592} z^{5}\right ) y \left (0\right )+\left (z -\frac {1}{18} z^{3}+\frac {5}{216} z^{4}-\frac {17}{2160} z^{5}\right ) D\left (y \right )\left (0\right )+O\left (z^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 63

AsymptoticDSolveValue[(z^2+5*z+6)*D[y[z],{z,2}]+2*y[z]==0,y[z],{z,0,"6"-1}]
 

\[ y(z)\to c_2 \left (-\frac {17 z^5}{2160}+\frac {5 z^4}{216}-\frac {z^3}{18}+z\right )+c_1 \left (\frac {5 z^5}{2592}-\frac {13 z^4}{1296}+\frac {5 z^3}{108}-\frac {z^2}{6}+1\right ) \]