73.23.17 problem 33.5 (e)

Internal problem ID [15663]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.5 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:50 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

Order:=6; 
dsolve((4-x^2)*diff(y(x),x$2)-5*x*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {3}{8} x^{2}+\frac {15}{128} x^{4}\right ) y \left (0\right )+\left (x +\frac {1}{3} x^{3}+\frac {1}{10} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

AsymptoticDSolveValue[(4-x^2)*D[y[x],{x,2}]-5*x*D[y[x],x]-3*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {x^5}{10}+\frac {x^3}{3}+x\right )+c_1 \left (\frac {15 x^4}{128}+\frac {3 x^2}{8}+1\right ) \]