66.1.1 problem 1

Internal problem ID [15888]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:29:12 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = c_1 t +c_1 -1 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.124 (sec). Leaf size: 8

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

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