59.3.3 problem 8.1 (iii)

Internal problem ID [15002]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.1 (iii)
Date solved : Thursday, October 02, 2025 at 09:58:22 AM
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: 0.015 (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: 0.163 (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)
 

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