63.5.26 problem 15(a)

Internal problem ID [13029]
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 : Monday, March 31, 2025 at 07:31:26 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=diff(x(t),t) = 2/3*x(t)/t+2*t/x(t); 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x &= \sqrt {\left (6 t^{{2}/{3}}+c_1 \right ) t^{{4}/{3}}} \\ x &= -\sqrt {\left (6 t^{{2}/{3}}+c_1 \right ) t^{{4}/{3}}} \\ \end{align*}

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

ode=D[x[t],t]==2/(3*t)*x[t]+2*t/x[t]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.301 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*t/x(t) + Derivative(x(t), t) - 2*x(t)/(3*t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ \left [ x{\left (t \right )} = - \sqrt {C_{1} t^{\frac {4}{3}} + 6 t^{2}}, \ x{\left (t \right )} = \sqrt {C_{1} t^{\frac {4}{3}} + 6 t^{2}}\right ] \]