9.8.13 problem problem 13

Internal problem ID [1078]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number : problem 13
Date solved : Monday, January 27, 2025 at 04:33:00 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

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

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

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