80.3.7 problem 7

Internal problem ID [21171]
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 : 7
Date solved : Thursday, October 02, 2025 at 07:15:22 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ x = \frac {2}{t^{2}+2 c_1} \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to \frac {2}{t^2-2 c_1}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 8

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

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