66.5.7 problem 2 and 14(iii)

Internal problem ID [15980]
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(iii)
Date solved : Thursday, October 02, 2025 at 10:36:02 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 5

ode:=diff(y(t),t) = y(t)^2-4*y(t)-12; 
ic:=[y(0) = 6]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 6 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[y[t],t]==y[t]^2-4*y[t]-12; 
ic={y[0]==6}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 6 \end{align*}

✗ 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(0): 6} 
dsolve(ode,func=y(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions