18.3.3 problem Problem 16.3

Internal problem ID [3503]
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
Date solved : Monday, January 27, 2025 at 07:39:58 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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);
 

\[ y \left (z \right ) = c_{1} z^{3} \left (1-\frac {1}{6} z^{6}+\operatorname {O}\left (z^{7}\right )\right )+c_{2} \left (12-6 z^{6}+\operatorname {O}\left (z^{7}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 12

AsymptoticDSolveValue[z*D[y[z],{z,2}]-2*D[y[z],z]+9*z^5*y[z]==0,y[z],{z,0,"7"-1}]
 

\[ y(z)\to c_2 z^3+c_1 \]