80.3.52 problem 55

Internal problem ID [21216]
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 : 55
Date solved : Thursday, October 02, 2025 at 07:26:57 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} x&=x^{\prime } t +\frac {1}{x^{\prime }} \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 27

ode:=x(t) = t*diff(x(t),t)+1/diff(x(t),t); 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x &= -2 \sqrt {t} \\ x &= 2 \sqrt {t} \\ x &= t c_1 +\frac {1}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 41

ode=x[t]==t*D[x[t],t]+1/D[x[t],t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 t+\frac {1}{c_1}\\ x(t)&\to \text {Indeterminate}\\ x(t)&\to -2 \sqrt {t}\\ x(t)&\to 2 \sqrt {t} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t*Derivative(x(t), t) + x(t) - 1/Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(x(t), t) - (sqrt(-4*t + x(t)**2) + x(t))/(2*t) cannot