63.5.26 problem 15(a)

Internal problem ID [13100]
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)
Date solved : Tuesday, January 28, 2025 at 04:52:17 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (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 {\left (6 t^{{2}/{3}}+c_{1} \right ) t^{{4}/{3}}} \\ x \left (t \right ) &= -\sqrt {\left (6 t^{{2}/{3}}+c_{1} \right ) t^{{4}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.689 (sec). Leaf size: 47

DSolve[D[x[t],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*}