Internal problem ID [12906]
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 1.3 page 47
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-3 y \left (-y+1\right )=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t)=3*y(t)*(1-y(t)),y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{1+{\mathrm e}^{-3 t}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 20
DSolve[{y'[t]==3*y[t]*(1-y[t]),{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{3 t}}{e^{3 t}+1} \]