28.5.6 problem 9.6

Internal problem ID [4593]
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 : 9.6
Date solved : Monday, January 27, 2025 at 09:25:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\[ y \left (x \right ) = \left (1-\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x +\frac {1}{12} x^{4}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 28

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

\[ y(x)\to c_2 \left (\frac {x^4}{12}+x\right )+c_1 \left (1-\frac {x^3}{6}\right ) \]