87.15.14 problem 14

Internal problem ID [23562]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 115
Problem number : 14
Date solved : Friday, October 03, 2025 at 08:03:46 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 43

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

\[ y = \left (1-\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x -\frac {1}{24} x^{4}\right ) y^{\prime }\left (0\right )+\frac {y^{\prime \prime }\left (0\right ) x^{2}}{2}-\frac {y^{\prime \prime }\left (0\right ) x^{5}}{120}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 46

ode=D[y[x],{x,3}]+y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (x-\frac {x^4}{24}\right )+c_1 \left (1-\frac {x^3}{6}\right )+c_3 \left (\frac {x^2}{2}-\frac {x^5}{120}\right ) \]

✗ Sympy

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

Series solution not supported for ode of order > 2