64.14.2 problem 2

Internal problem ID [13561]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page 232
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 05:53:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+8 x y^{\prime }-4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 39

Order:=6; 
dsolve(diff(y(x),x$2)+8*x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 38

AsymptoticDSolveValue[D[y[x],{x,2}]+8*x*D[y[x],x]-4*y[x]==0,y[x],{x,0,"6"-1}]
 

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