84.32.5 problem 19.17

Internal problem ID [22313]
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. Supplementary problems
Problem number : 19.17
Date solved : Thursday, October 02, 2025 at 08:37:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+y&=x \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 49

Order:=6; 
ode:=(x^2+4)*diff(diff(y(x),x),x)+y(x) = x; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{8} x^{2}+\frac {1}{128} x^{4}\right ) y \left (0\right )+\left (x -\frac {1}{24} x^{3}+\frac {7}{1920} x^{5}\right ) y^{\prime }\left (0\right )+\frac {x^{3}}{24}-\frac {7 x^{5}}{1920}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 56

ode=(x^2+4)*D[y[x],{x,2}]+y[x]==x; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to -\frac {7 x^5}{1920}+\frac {x^3}{24}+c_2 \left (\frac {7 x^5}{1920}-\frac {x^3}{24}+x\right )+c_1 \left (\frac {x^4}{128}-\frac {x^2}{8}+1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (x**2 + 4)*Derivative(y(x), (x, 2)) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : ODE -x + (x**2 + 4)*Derivative(y(x), (x, 2)) + y(x) does not match hint 2nd_power_series_regular