10.4.6 problem 7

Internal problem ID [1187]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 12:17:38 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

\[ y = \frac {1+k \left (t +c_1 \right )}{k \left (t +c_1 \right )} \]

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.198 (sec). Leaf size: 14

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

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