Internal problem ID [2027]
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 16.9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 z y^{\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: 32
Order:=6; dsolve(diff(y(z),z$2)-2*z*diff(y(z),z)-2*y(z)=0,y(z),type='series',z=0);
\[ y \relax (z ) = \left (1+z^{2}+\frac {1}{2} z^{4}\right ) y \relax (0)+\left (z +\frac {2}{3} z^{3}+\frac {4}{15} z^{5}\right ) D\relax (y )\relax (0)+O\left (z^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[y''[z]-2*z*y'[z]-2*y[z]==0,y[z],{z,0,5}]
\[ y(z)\to c_2 \left (\frac {4 z^5}{15}+\frac {2 z^3}{3}+z\right )+c_1 \left (\frac {z^4}{2}+z^2+1\right ) \]