63.5.32 problem 16-b(i)

Internal problem ID [13106]
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(i)
Date solved : Tuesday, January 28, 2025 at 04:52:34 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 66

dsolve(x(t)^3+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 {\left (-c_{1} t^{2}\right )^{{1}/{3}}}{t} \\ x \left (t \right ) &= -\frac {\left (-c_{1} t^{2}\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 t} \\ x \left (t \right ) &= \frac {\left (-c_{1} t^{2}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

DSolve[x[t]^3+3*t*x[t]^2*D[x[t],t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 0 \\ x(t)\to \frac {c_1}{\sqrt [3]{t}} \\ x(t)\to 0 \\ \end{align*}