28.5.18 problem 9.18

Internal problem ID [4605]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 9. Series Solutions of Differential Equations. Problems at page 426
Problem number : 9.18
Date solved : Monday, January 27, 2025 at 09:26:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 32

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

\[ y \left (x \right ) = c_{1} \left (1+\frac {1}{6} x^{2}+\frac {1}{120} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1+\frac {1}{2} x^{2}+\frac {1}{24} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 42

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

\[ y(x)\to c_1 \left (\frac {x^3}{24}+\frac {x}{2}+\frac {1}{x}\right )+c_2 \left (\frac {x^4}{120}+\frac {x^2}{6}+1\right ) \]