73.23.19 problem 33.5 (g)

Internal problem ID [15665]
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 (g)
Date solved : Tuesday, January 28, 2025 at 08:03:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+6 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: 34

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 33

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

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