30.1.8 problem 8

Internal problem ID [7398]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:30:29 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=3 x t^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(x(t),t) = 3*x(t)*t^2; 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[x[t],t]==3*x[t]*t^2; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*t**2*x(t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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