Internal problem ID [2026]
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 16.8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {z y^{\prime \prime }-2 y^{\prime }+y z=0} \end {gather*} With the expansion point for the power series method at \(z = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 32
Order:=6; dsolve(z*diff(y(z),z$2)-2*diff(y(z),z)+z*y(z)=0,y(z),type='series',z=0);
\[ y \relax (z ) = c_{1} z^{3} \left (1-\frac {1}{10} z^{2}+\frac {1}{280} z^{4}+\mathrm {O}\left (z^{6}\right )\right )+c_{2} \left (12+6 z^{2}-\frac {3}{2} z^{4}+\mathrm {O}\left (z^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 44
AsymptoticDSolveValue[z*y''[z]-2*y'[z]+z*y[z]==0,y[z],{z,0,5}]
\[ y(z)\to c_1 \left (-\frac {z^4}{8}+\frac {z^2}{2}+1\right )+c_2 \left (\frac {z^7}{280}-\frac {z^5}{10}+z^3\right ) \]