80.3.47 problem 50

Internal problem ID [21211]
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 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 50
Date solved : Thursday, October 02, 2025 at 07:26:51 PM
CAS classification : [_quadrature]

\begin{align*} {x^{\prime }}^{2}&=4-4 x \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 22

ode:=diff(x(t),t)^2 = 4-4*x(t); 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x &= 1 \\ x &= -\left (t -c_1 +1\right ) \left (t -c_1 -1\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 53

ode=D[x[t],t]^2==4*(1-x[t]); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -t^2-c_1 t+1-\frac {c_1{}^2}{4}\\ x(t)&\to -t^2+c_1 t+1-\frac {c_1{}^2}{4}\\ x(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.265 (sec). Leaf size: 31

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

\[ \left [ x{\left (t \right )} = - \frac {C_{1}^{2}}{4} + C_{1} t - t^{2} + 1, \ - 2 \sqrt {1 - x{\left (t \right )}} = C_{1} + 2 t\right ] \]