72.4.7 problem 14

Internal problem ID [14605]
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 1.5 page 71
Problem number : 14
Date solved : Thursday, March 13, 2025 at 04:08:36 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.296 (sec). Leaf size: 23

ode:=diff(y(t),t) = 1/(y(t)+1)/(t-2); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -1+\sqrt {1-2 i \pi +2 \ln \left (t -2\right )-2 \ln \left (2\right )} \]

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 28

ode=D[y[t],t]==1/( (y[t]+1)*(t-2)); 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -1+\sqrt {2 \log (t-2)-2 i \pi +1-\log (4)} \]

✓ Sympy. Time used: 0.550 (sec). Leaf size: 24

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

\[ y{\left (t \right )} = \sqrt {2 \log {\left (t - 2 \right )} - \log {\left (4 \right )} + 1 - 2 i \pi } - 1 \]