72.5.6 problem 2 and 14(ii)

Internal problem ID [14621]
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 : Monday, March 31, 2025 at 12:43:56 PM
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*}

✓ Maple. Time used: 0.100 (sec). Leaf size: 27

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

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

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

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**2 + 4*y(t) + Derivative(y(t), t) + 12,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants