57.5.20 problem 5

Internal problem ID [14375]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:34:18 AM
CAS classification : [_separable]

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

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

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

\[ x = c_1 \,{\mathrm e}^{t^{2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

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

\begin{align*} x(t)&\to c_1 e^{t^2}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.135 (sec). Leaf size: 8

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

\[ x{\left (t \right )} = C_{1} e^{t^{2}} \]