80.12.11 problem 19

Internal problem ID [21444]
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 13. Boundary value problems. Excercise 13.5 at page 291
Problem number : 19
Date solved : Friday, October 03, 2025 at 07:52:04 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ x \left (\pi \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 5

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

\[ x = 0 \]

✗ Mathematica

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

{}

✗ Sympy

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