65.3.3 problem 8.1 (iii)

Internal problem ID [13642]
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 : Wednesday, March 05, 2025 at 10:06:12 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.024 (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: 0.259 (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)
 

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