Internal problem ID [12934]
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 1.4 page 61
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {w^{\prime }-\left (3-w\right ) \left (w+1\right )=0} \] With initial conditions \begin {align*} [w \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 21
dsolve([diff(w(t),t)=(3-w(t))*(w(t)+1),w(0) = 0],w(t), singsol=all)
\[ w \left (t \right ) = \frac {3 \,{\mathrm e}^{4 t}-3}{3+{\mathrm e}^{4 t}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 23
DSolve[{w'[t]==(3-w[t])*(w[t]+1),{w[0]==0}},w[t],t,IncludeSingularSolutions -> True]
\[ w(t)\to \frac {3 \left (e^{4 t}-1\right )}{e^{4 t}+3} \]