72.2.16 problem 16 (i)

Internal problem ID [14651]
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 (i)
Date solved : Tuesday, January 28, 2025 at 06:46:27 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = \frac {1}{-1+{\mathrm e}^{-t} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 40

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

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