35.9.15 problem 8, using series method

Internal problem ID [6250]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 8, using series method
Date solved : Monday, January 27, 2025 at 01:50:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 28

Order:=6; 
dsolve((x^2+2*x)*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 23

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

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