Internal problem ID [11434]
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: 15(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x^{\prime }-\frac {2 x}{3 t}-\frac {2 t}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(x(t),t)=2/(3*t)*x(t)+2*t/x(t),x(t), singsol=all)
\begin{align*} x \left (t \right ) = \sqrt {t^{\frac {4}{3}} c_{1} +6 t^{2}} x \left (t \right ) = -\sqrt {t^{\frac {4}{3}} c_{1} +6 t^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 5.087 (sec). Leaf size: 47
DSolve[x'[t]==2/(3*t)*x[t]+2*t/x[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\sqrt {6 t^2+c_1 t^{4/3}} x(t)\to \sqrt {6 t^2+c_1 t^{4/3}} \end{align*}