Internal problem ID [2024]
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 16.4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f=0} \end {gather*} With the expansion point for the power series method at \(z = 0\).
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 52
Order:=6; dsolve(diff(f(z),z$2)+2*(z-1)*diff(f(z),z)+4*f(z)=0,f(z),type='series',z=0);
\[ f \relax (z ) = \left (1-2 z^{2}-\frac {4}{3} z^{3}+\frac {2}{3} z^{4}+\frac {14}{15} z^{5}\right ) f \relax (0)+\left (z +z^{2}-\frac {1}{3} z^{3}-\frac {5}{6} z^{4}-\frac {1}{6} z^{5}\right ) D\relax (f )\relax (0)+O\left (z^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 127
AsymptoticDSolveValue[f''[z]+2*(z-a)*f'[z]+4*f[z]==0,f[z],{z,0,5}]
\[ f(z)\to c_1 \left (-\frac {4}{15} a^3 z^5-\frac {2 a^2 z^4}{3}+\frac {6 a z^5}{5}-\frac {4 a z^3}{3}+\frac {4 z^4}{3}-2 z^2+1\right )+c_2 \left (\frac {2 a^4 z^5}{15}+\frac {a^3 z^4}{3}-\frac {4 a^2 z^5}{5}+\frac {2 a^2 z^3}{3}-\frac {7 a z^4}{6}+a z^2+\frac {z^5}{2}-z^3+z\right ) \]