80.8.24 problem 30

Internal problem ID [21381]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 8. Qualitative analysis of 2 by 2 systems and nonlinear second order equations. Excercise 8.5 at page 184
Problem number : 30
Date solved : Thursday, October 02, 2025 at 07:30:31 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} x^{\prime \prime }-x+3 x^{2}&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ x^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.100 (sec). Leaf size: 27

ode:=diff(diff(x(t),t),t)-x(t)+3*x(t)^2 = 0; 
ic:=[x(0) = 0, D(x)(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \operatorname {RootOf}\left (-\int _{0}^{\textit {\_Z}}\frac {1}{\sqrt {-2 \textit {\_a}^{3}+\textit {\_a}^{2}+1}}d \textit {\_a} +t \right ) \]

✗ Mathematica

ode=D[x[t],{t,2}]-x[t]+3*x[t]^2==0; 
ic={x[0]==0,Derivative[1][x][0] ==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t)**2 - x(t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 0, Subs(Derivative(x(t), t), t, 0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

Timed Out