50.22.2 problem 1(b)

Internal problem ID [8145]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert. (A) Drill Exercises . Page 194
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:44:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 48

Order:=8; 
dsolve(diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{2} x^{2}-\frac {1}{24} x^{4}-\frac {1}{240} x^{6}\right ) y \left (0\right )+y^{\prime }\left (0\right ) x +\frac {x^{3}}{6}+\frac {x^{5}}{60}+\frac {x^{7}}{630}+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 55

AsymptoticDSolveValue[D[y[x],{x,2}]-x*D[y[x],x]+y[x]==x,y[x],{x,0,"8"-1}]
 

\[ y(x)\to \frac {x^7}{630}+\frac {x^5}{60}+\frac {x^3}{6}+c_1 \left (-\frac {x^6}{240}-\frac {x^4}{24}-\frac {x^2}{2}+1\right )+c_2 x \]