90.3.11 problem 11

Internal problem ID [25075]
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 41
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:49:18 PM
CAS classification : [_separable]

\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \end{align*}

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

ode:=1-y(t)^2-t*y(t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 87

ode=(1-y[t]^2)-t*y[t]*D[y[t],{t,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {\sqrt {t^2+e^{2 c_1}}}{t}\\ y(t)&\to \frac {\sqrt {t^2+e^{2 c_1}}}{t}\\ y(t)&\to -1\\ y(t)&\to 1\\ y(t)&\to -\frac {\sqrt {t^2}}{t}\\ y(t)&\to \frac {\sqrt {t^2}}{t} \end{align*}

✓ Sympy. Time used: 0.292 (sec). Leaf size: 26

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

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