12.12.27 problem 33

Internal problem ID [1881]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN ORDINARY POINT I. Exercises 7.2. Page 329
Problem number : 33
Date solved : Monday, January 27, 2025 at 05:37:46 AM
CAS classification : [[_Emden, _Fowler]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

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

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

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