80.1.12 problem 12

Internal problem ID [21130]
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 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 12
Date solved : Thursday, October 02, 2025 at 07:09:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ x = c_1 \,{\mathrm e}^{-\frac {t^{3}}{3}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to c_1 e^{-\frac {t^3}{3}}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = C_{1} e^{- \frac {t^{3}}{3}} \]