Internal problem ID [2023]
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 16.3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y=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: 28
Order:=7; dsolve(z*diff(y(z),z$2)-2*diff(y(z),z)+9*z^5*y(z)=0,y(z),type='series',z=0);
\[ y \relax (z ) = c_{1} z^{3} \left (1-\frac {1}{6} z^{6}+\mathrm {O}\left (z^{7}\right )\right )+c_{2} \left (12-6 z^{6}+\mathrm {O}\left (z^{7}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 12
AsymptoticDSolveValue[z*y''[z]-2*y'[z]+9*z^5*y[z]==0,y[z],{z,0,6}]
\[ y(z)\to c_2 z^3+c_1 \]