73.23.31 problem 33.11 (e)

Internal problem ID [15598]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.11 (e)
Date solved : Thursday, March 13, 2025 at 06:12:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+x y&=\sin \left (x \right ) \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

Order:=5; 
ode:=diff(diff(y(x),x),x)+x*y(x) = sin(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{4}\right ) y^{\prime }\left (0\right )+\frac {x^{3}}{6}+O\left (x^{5}\right ) \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+x*y[x]==Sin[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,4}]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) - sin(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=5)
 

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