72.2.18 problem 16 (iii)

Internal problem ID [14653]
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 : 16 (iii)
Date solved : Tuesday, January 28, 2025 at 06:46:31 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.398 (sec). Leaf size: 18

dsolve(diff(y(t),t)=y(t)^3+y(t)^2,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.194 (sec). Leaf size: 40

DSolve[D[y[t],t]==y[t]^3+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2 (K[1]+1)}dK[1]\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}