73.1.9 problem 2 (iii)

Internal problem ID [19782]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 2 (iii)
Date solved : Thursday, October 02, 2025 at 04:43:20 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

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

\[ x = 1 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[x[t],t]==(x[t]-1)^2; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 1 \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions