Internal problem ID [14252]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-\frac {3 x t^{2}}{-t^{3}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(x(t),t)=3*x(t)*t^2/(1-t^3),x(t), singsol=all)
\[ x \left (t \right ) = \frac {c_{1}}{t^{3}-1} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 20
DSolve[x'[t]==3*x[t]*t^2/(1-t^3),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_1}{t^3-1} \\ x(t)\to 0 \\ \end{align*}