82.2.20 problem 24-21

Internal problem ID [21781]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 24. Power series about an ordinary point. Page 719
Problem number : 24-21
Date solved : Thursday, October 02, 2025 at 08:02:05 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }+x^{2}&=0 \end{align*}

Using series method with expansion around

\begin{align*} -{\frac {1}{2}} \end{align*}

With initial conditions

\begin{align*} x \left (-\frac {1}{2}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 5

Order:=6; 
ode:=diff(x(t),t)+x(t)^2 = 0; 
ic:=[x(-1/2) = 0]; 
dsolve([ode,op(ic)],x(t),type='series',t=-1/2);
 

\[ x = 0 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 4

ode=D[x[t],t]+x[t]^2==0; 
ic={x[-1/2]==0}; 
AsymptoticDSolveValue[{ode,ic},x[t],{t,-1/2,5}]
 

\[ x(t)\to 0 \]

✓ Sympy. Time used: 0.111 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t)**2 + Derivative(x(t), t),0) 
ics = {x(-1/2): 0} 
dsolve(ode,func=x(t),ics=ics,hint="1st_power_series",x0=-1/2,n=6)
 

\[ x{\left (t \right )} = O\left (t^{6}\right ) \]