Internal problem ID [1678]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-k \left (a -y\right ) \left (b -y\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.264 (sec). Leaf size: 35
dsolve([diff(y(t),t) = k*(a-y(t))*(b-y(t)),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {a b \left ({\mathrm e}^{t k \left (a -b \right )}-1\right )}{{\mathrm e}^{t k \left (a -b \right )} a -b} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 40
DSolve[{y'[t] == k*(a-y[t])*(b-y[t]),y[0]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {a (a-b) e^{a k t}}{b e^{b k t}-a e^{a k t}}+a \\ \end{align*}