63.5.35 problem 16-b(iv)

Internal problem ID [13109]
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 : Tuesday, January 28, 2025 at 04:52:59 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 35

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

\begin{align*} x \left (t \right ) &= 0 \\ x \left (t \right ) &= -\frac {\sqrt {-6 \ln \left (t \right )+9 c_{1}}}{3} \\ x \left (t \right ) &= \frac {\sqrt {-6 \ln \left (t \right )+9 c_{1}}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 51

DSolve[x[t]+3*t*x[t]^2*D[x[t],t]==0,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*}