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 : Monday, January 27, 2025 at 04:43:25 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[t],t]== -k*(-1+y[t])^2,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*}