57.5.35 problem 16-b(iv)

Internal problem ID [14390]
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 : 16-b(iv)
Date solved : Thursday, October 02, 2025 at 09:36:32 AM
CAS classification : [_separable]

\begin{align*} x+3 t x^{2} x^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=x(t)+3*t*x(t)^2*diff(x(t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x &= 0 \\ x &= -\frac {\sqrt {-6 \ln \left (t \right )+9 c_1}}{3} \\ x &= \frac {\sqrt {-6 \ln \left (t \right )+9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 51

ode=x[t]+3*t*x[t]^2*D[x[t],t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 0\\ x(t)&\to -\sqrt {-\frac {2 \log (t)}{3}+2 c_1}\\ x(t)&\to \sqrt {-\frac {2 \log (t)}{3}+2 c_1}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.357 (sec). Leaf size: 32

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

\[ \left [ x{\left (t \right )} = - \frac {\sqrt {C_{1} - 6 \log {\left (t \right )}}}{3}, \ x{\left (t \right )} = \frac {\sqrt {C_{1} - 6 \log {\left (t \right )}}}{3}, \ x{\left (t \right )} = 0\right ] \]