Internal problem ID [10412]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{3}+3 x^{\prime } t x^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 88
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 )^{\frac {1}{3}}}{t} \\ x \left (t \right ) = -\frac {\left (-c_{1} t^{2}\right )^{\frac {1}{3}}}{2 t}-\frac {i \sqrt {3}\, \left (-c_{1} t^{2}\right )^{\frac {1}{3}}}{2 t} \\ x \left (t \right ) = -\frac {\left (-c_{1} t^{2}\right )^{\frac {1}{3}}}{2 t}+\frac {i \sqrt {3}\, \left (-c_{1} t^{2}\right )^{\frac {1}{3}}}{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 23
DSolve[x[t]^3+3*t*x[t]^2*x'[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*}