63.4.14 problem 4(f)

Internal problem ID [12978]
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(f)
Date solved : Wednesday, March 05, 2025 at 08:55:44 PM
CAS classification : [_separable]

\begin{align*} \left (1+t \right ) x^{\prime }+x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=(t+1)*diff(x(t),t)+x(t)^2 = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = \frac {1}{\ln \left (t +1\right )+c_{1}} \]

✓ Mathematica. Time used: 0.164 (sec). Leaf size: 21

ode=(1+t)*D[x[t],t]+x[t]^2==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to \frac {1}{\log (t+1)-c_1} \\ x(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 12

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

\[ x{\left (t \right )} = - \frac {1}{C_{1} - \log {\left (t + 1 \right )}} \]