Internal problem ID [2029]
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 16.11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}=0} \end {gather*} With the expansion point for the power series method at \(z = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 69
Order:=6; dsolve(z*diff(y(z),z$2)+(2*z-3)*diff(y(z),z)+4/z*y(z)=0,y(z),type='series',z=0);
\[ y \relax (z ) = z^{2} \left (\left (c_{2} \ln \relax (z )+c_{1}\right ) \left (1-4 z +6 z^{2}-\frac {16}{3} z^{3}+\frac {10}{3} z^{4}-\frac {8}{5} z^{5}+\mathrm {O}\left (z^{6}\right )\right )+\left (6 z -13 z^{2}+\frac {124}{9} z^{3}-\frac {173}{18} z^{4}+\frac {374}{75} z^{5}+\mathrm {O}\left (z^{6}\right )\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 116
AsymptoticDSolveValue[z*y''[z]+(2*z-3)*y'[z]+4/z*y[z]==0,y[z],{z,0,5}]
\[ y(z)\to c_1 \left (-\frac {8 z^5}{5}+\frac {10 z^4}{3}-\frac {16 z^3}{3}+6 z^2-4 z+1\right ) z^2+c_2 \left (\left (\frac {374 z^5}{75}-\frac {173 z^4}{18}+\frac {124 z^3}{9}-13 z^2+6 z\right ) z^2+\left (-\frac {8 z^5}{5}+\frac {10 z^4}{3}-\frac {16 z^3}{3}+6 z^2-4 z+1\right ) z^2 \log (z)\right ) \]