57.4.9 problem 4(a)

Internal problem ID [14333]
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 1.3.1 Separable equations. Exercises page 26
Problem number : 4(a)
Date solved : Thursday, October 02, 2025 at 09:31:41 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {2 x}{t +1} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=diff(x(t),t) = 2*x(t)/(t+1); 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \left (t +1\right )^{2} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[x[t],t]==2*x[t]/(t+1); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 (t+1)^2\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - 2*x(t)/(t + 1),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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