80.3.11 problem 11

Internal problem ID [21175]
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 : 11
Date solved : Thursday, October 02, 2025 at 07:15:33 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

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

\[ x = \frac {6}{2 t^{3}+1} \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 16

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

\begin{align*} x(t)&\to \frac {6}{2 t^3+1} \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = \frac {3}{t^{3} + \frac {1}{2}} \]