74.5.23 problem 23

Internal problem ID [15987]
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
Date solved : Tuesday, January 28, 2025 at 08:25:44 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.036 (sec). Leaf size: 20

DSolve[D[x[t],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*}