43.1.3 problem 7.2.3

Internal problem ID [6848]
Book : Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section : Chapter 7. POWER SERIES METHODS. 7.2.1 Exercises. page 290
Problem number : 7.2.3
Date solved : Monday, January 27, 2025 at 02:31:39 PM
CAS classification : [[_Emden, _Fowler]]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 69

Order:=6; 
dsolve(diff(y(x),x$2)-x*y(x)=0,y(x),type='series',x=1);
 

\[ y = \left (1+\frac {\left (x -1\right )^{2}}{2}+\frac {\left (x -1\right )^{3}}{6}+\frac {\left (x -1\right )^{4}}{24}+\frac {\left (x -1\right )^{5}}{30}\right ) y \left (1\right )+\left (x -1+\frac {\left (x -1\right )^{3}}{6}+\frac {\left (x -1\right )^{4}}{12}+\frac {\left (x -1\right )^{5}}{120}\right ) y^{\prime }\left (1\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 78

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

\[ y(x)\to c_1 \left (\frac {1}{30} (x-1)^5+\frac {1}{24} (x-1)^4+\frac {1}{6} (x-1)^3+\frac {1}{2} (x-1)^2+1\right )+c_2 \left (\frac {1}{120} (x-1)^5+\frac {1}{12} (x-1)^4+\frac {1}{6} (x-1)^3+x-1\right ) \]