80.12.5 problem 6 (a)

Internal problem ID [21438]
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 : 6 (a)
Date solved : Friday, October 03, 2025 at 07:52:01 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} x^{\prime \prime }+4 x^{3}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.142 (sec). Leaf size: 41

ode:=diff(diff(x(t),t),t)+4*x(t)^3 = 0; 
ic:=[x(0) = 0, x(b) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \operatorname {RootOf}\left (\operatorname {JacobiSN}\left (\textit {\_Z} \sqrt {2}\, b , i\right ) \textit {\_Z} -1\right ) \operatorname {JacobiSN}\left (\sqrt {2}\, t \operatorname {RootOf}\left (\operatorname {JacobiSN}\left (\textit {\_Z} \sqrt {2}\, b , i\right ) \textit {\_Z} -1\right ), i\right ) \]

✗ Mathematica

ode=D[x[t],{t,2}]+4*x[t]^3==0; 
ic={x[0]==0,x[b]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
t = symbols("t") 
b = symbols("b") 
x = Function("x") 
ode = Eq(4*x(t)**3 + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 0, x(b): 1} 
dsolve(ode,func=x(t),ics=ics)