80.3.38 problem 41

Internal problem ID [21202]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 41
Date solved : Thursday, October 02, 2025 at 07:26:24 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\begin{align*} x &= \sqrt {c_1 \,t^{4}+1}\, t \\ x &= -\sqrt {c_1 \,t^{4}+1}\, t \\ \end{align*}

✓ Mathematica. Time used: 0.468 (sec). Leaf size: 39

ode=D[x[t],t]==(3*x[t]^2-2*t^2)/(t*x[t]); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\sqrt {t^2+c_1 t^6}\\ x(t)&\to \sqrt {t^2+c_1 t^6} \end{align*}

✓ Sympy. Time used: 0.245 (sec). Leaf size: 29

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

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