Internal problem ID [11443]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x+3 x^{\prime } t x^{2}=0} \]
✓ Solution by Maple
Time used: 0.032 (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: 0.113 (sec). Leaf size: 51
DSolve[x[t]+3*t*x[t]^2*x'[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*}