52.1.29 problem 26 (a)

Internal problem ID [8246]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 26 (a)
Date solved : Sunday, March 30, 2025 at 12:49:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-x y&=1 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 49

Order:=8; 
ode:=diff(diff(y(x),x),x)-x*y(x) = 1; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{6} x^{3}+\frac {1}{180} x^{6}\right ) y \left (0\right )+\left (x +\frac {1}{12} x^{4}+\frac {1}{504} x^{7}\right ) y^{\prime }\left (0\right )+\frac {x^{2}}{2}+\frac {x^{5}}{40}+O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 56

ode=D[y[x],{x,2}]-x*y[x]==1; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to \frac {x^5}{40}+\frac {x^2}{2}+c_2 \left (\frac {x^7}{504}+\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^6}{180}+\frac {x^3}{6}+1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=8)
 

ValueError : ODE -x*y(x) + Derivative(y(x), (x, 2)) - 1 does not match hint 2nd_power_series_regular