Internal problem ID [537]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+k \left (y-1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(diff(y(t),t) = -k*(-1+y(t))^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} k +t k +1}{k \left (t +c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 22
DSolve[y'[t]== -k*(-1+y[t])^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 1+\frac {1}{k t-c_1} \\ y(t)\to 1 \\ \end{align*}