90.4.9 problem 10

Internal problem ID [25104]
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 59
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:50:18 PM
CAS classification : [_separable]

\begin{align*} t \left (t +1\right ) y^{\prime }&=y+2 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {t c_1 -2}{t +1} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.155 (sec). Leaf size: 14

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

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