Internal problem ID [2032]
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 16.13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{z^{3}}=0} \end {gather*} With the expansion point for the power series method at \(z = 0\).
✗ Solution by Maple
Order:=6; dsolve(diff(y(z),z$2)+1/z^3*y(z)=0,y(z),type='series',z=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 222
AsymptoticDSolveValue[y''[z]+1/z^3*y[z]==0,y[z],{z,0,5}]
\[ y(z)\to c_1 e^{-\frac {2 i}{\sqrt {z}}} z^{3/4} \left (-\frac {468131288625 i z^{9/2}}{8796093022208}+\frac {66891825 i z^{7/2}}{4294967296}-\frac {72765 i z^{5/2}}{8388608}+\frac {105 i z^{3/2}}{8192}+\frac {33424574007825 z^5}{281474976710656}-\frac {14783093325 z^4}{549755813888}+\frac {2837835 z^3}{268435456}-\frac {4725 z^2}{524288}+\frac {15 z}{512}-\frac {3 i \sqrt {z}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {z}}} z^{3/4} \left (\frac {468131288625 i z^{9/2}}{8796093022208}-\frac {66891825 i z^{7/2}}{4294967296}+\frac {72765 i z^{5/2}}{8388608}-\frac {105 i z^{3/2}}{8192}+\frac {33424574007825 z^5}{281474976710656}-\frac {14783093325 z^4}{549755813888}+\frac {2837835 z^3}{268435456}-\frac {4725 z^2}{524288}+\frac {15 z}{512}+\frac {3 i \sqrt {z}}{16}+1\right ) \]