84.31.7 problem 19.8

Internal problem ID [22305]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 19. Power series solutions about an ordinary point. Solved problems. Page 98
Problem number : 19.8
Date solved : Thursday, October 02, 2025 at 08:37:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y x&=2 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

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

\[ y = \left (1-\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{4}\right ) y^{\prime }\left (0\right )+x^{2}-\frac {x^{5}}{20}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+x*y[x]==2; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to -\frac {x^5}{20}+c_2 \left (x-\frac {x^4}{12}\right )+c_1 \left (1-\frac {x^3}{6}\right )+x^2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + Derivative(y(x), (x, 2)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

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