68.7.24 problem 24

Internal problem ID [17388]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 24
Date solved : Thursday, October 02, 2025 at 02:15:51 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y+\left (t +y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.246 (sec). Leaf size: 84

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

\begin{align*} y(t)&\to -t-\sqrt {t^2+e^{2 c_1}}\\ y(t)&\to -t+\sqrt {t^2+e^{2 c_1}}\\ y(t)&\to 0\\ y(t)&\to -\sqrt {t^2}-t\\ y(t)&\to \sqrt {t^2}-t \end{align*}

✓ Sympy. Time used: 0.573 (sec). Leaf size: 26

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

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