72.3.9 problem 9

Internal problem ID [14673]
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 : 9
Date solved : Tuesday, January 28, 2025 at 06:47:17 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{5}} \end{align*}

✓ Solution by Maple

Time used: 3.642 (sec). Leaf size: 17

dsolve([diff(y(t),t)=y(t)^2-y(t)^3,y(0) = 1/5],y(t), singsol=all)
 

\[ y = \frac {1}{\operatorname {LambertW}\left (4 \,{\mathrm e}^{-t +4}\right )+1} \]

✓ Solution by Mathematica

Time used: 0.311 (sec). Leaf size: 31

DSolve[{D[y[t],t]==y[t]^2-y[t]^3,{y[0]==2/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\log (1-\text {$\#$1})-\log (\text {$\#$1})\&\right ][-t+5+\log (4)] \]