Internal problem ID [2031]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(z = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
Order:=6; dsolve((z^2+5*z+7)*diff(y(z),z$2)+2*y(z)=0,y(z),type='series',z=0);
\[ y \relax (z ) = \left (1-\frac {1}{7} z^{2}+\frac {5}{147} z^{3}-\frac {11}{2058} z^{4}+\frac {5}{14406} z^{5}\right ) y \relax (0)+\left (z -\frac {1}{21} z^{3}+\frac {5}{294} z^{4}-\frac {47}{10290} z^{5}\right ) D\relax (y )\relax (0)+O\left (z^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(z^2+5*z+7)*y''[z]+2*y[z]==0,y[z],{z,0,5}]
\[ y(z)\to c_2 \left (-\frac {47 z^5}{10290}+\frac {5 z^4}{294}-\frac {z^3}{21}+z\right )+c_1 \left (\frac {5 z^5}{14406}-\frac {11 z^4}{2058}+\frac {5 z^3}{147}-\frac {z^2}{7}+1\right ) \]