45.1.9 problem 21

Internal problem ID [7209]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page 230
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:48:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+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)+x^2*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 28

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

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