90.3.20 problem 20

Internal problem ID [25084]
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 : 20
Date solved : Thursday, October 02, 2025 at 11:49:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

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

\begin{align*} y &= \sqrt {-t^{2}-2 \ln \left (t \right )+c_1} \\ y &= -\sqrt {-t^{2}-2 \ln \left (t \right )+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.237 (sec). Leaf size: 32

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

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