72.5.6 problem 2 and 14(ii)

Internal problem ID [14692]
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 1.6 page 89
Problem number : 2 and 14(ii)
Date solved : Tuesday, January 28, 2025 at 07:11:37 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.217 (sec). Leaf size: 27

dsolve([diff(y(t),t)=y(t)^2-4*y(t)-12,y(1) = 0],y(t), singsol=all)
 

\[ y = \frac {6-6 \,{\mathrm e}^{-8+8 t}}{3 \,{\mathrm e}^{-8+8 t}+1} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 32

DSolve[{D[y[t],t]==y[t]^2-4*y[t]-12,{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {6 e^8-6 e^{8 t}}{3 e^{8 t}+e^8} \]