90.7.14 problem 14

Internal problem ID [25168]
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 99
Problem number : 14
Date solved : Thursday, October 02, 2025 at 11:56:09 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.170 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.256 (sec). Leaf size: 48

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

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

✓ Sympy. Time used: 0.709 (sec). Leaf size: 29

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

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