Internal problem ID [12951]
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 1.6 page 89
Problem number: 1 and 13 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-3 y \left (y-2\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(t),t)=3*y(t)*(y(t)-2),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2}{1+{\mathrm e}^{6 t}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 16
DSolve[{y'[t]==3*y[t]*(y[t]-2),{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2}{e^{6 t}+1} \]