72.4.2 problem 6

Internal problem ID [14679]
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 1.5 page 71
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:52:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 5

dsolve([diff(y(t),t)=y(t)*(y(t)-1)*(y(t)-3),y(0) = 0],y(t), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{D[y[t],t]==y[t]*(y[t]-1)*(y[t]-3),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 0 \]