66.1.17 problem 20

Internal problem ID [15904]
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 : 20
Date solved : Thursday, October 02, 2025 at 10:29:37 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= -1-\sqrt {1+2 \ln \left (t +1\right )+2 c_1} \\ y &= -1+\sqrt {1+2 \ln \left (t +1\right )+2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.205 (sec). Leaf size: 32

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

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