80.3.9 problem 9

Internal problem ID [21173]
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 : 9
Date solved : Thursday, October 02, 2025 at 07:15:27 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} x \left (\sqrt {2}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 11

ode:=diff(x(t),t) = t/x(t); 
ic:=[x(2^(1/2)) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \sqrt {t^{2}-1} \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 14

ode=D[x[t],t]==t/x[t]; 
ic={x[Sqrt[2]]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \sqrt {t^2-1} \end{align*}

✓ Sympy. Time used: 0.165 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t/x(t) + Derivative(x(t), t),0) 
ics = {x(sqrt(2)): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \sqrt {t^{2} - 1} \]