90.5.6 problem 6

Internal problem ID [25125]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:52:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=2 \,{\mathrm e} \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 14

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

\[ y = \sqrt {2 \ln \left (t \right )+2}\, t \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 17

ode=D[y[t],{t,1}] == (t^2+y[t]^2)/(t*y[t]); 
ic={y[Exp[1]]==Exp[1]}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.255 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = t \sqrt {2 \log {\left (t \right )} - 1} \]