20.24.11 problem Problem 11

Internal problem ID [3996]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page 739
Problem number : Problem 11
Date solved : Monday, January 27, 2025 at 08:05:55 AM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 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((1-4*x^2)*diff(y(x),x$2)-20*x*diff(y(x),x)-16*y(x)=0,y(x),type='series',x=0);
 

\[ y \left (x \right ) = \left (1+8 x^{2}+\frac {128}{3} x^{4}\right ) y \left (0\right )+\left (30 x^{5}+6 x^{3}+x \right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 36

AsymptoticDSolveValue[(1-4*x^2)*D[y[x],{x,2}]-20*x*D[y[x],x]-16*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (30 x^5+6 x^3+x\right )+c_1 \left (\frac {128 x^4}{3}+8 x^2+1\right ) \]