74.4.70 problem 67

Internal problem ID [15884]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 67
Date solved : Thursday, March 13, 2025 at 06:56:00 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 24

ode:=diff(y(t),t) = 12+4*y(t)-y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {6 \,{\mathrm e}^{8 t} c_{1} +2}{{\mathrm e}^{8 t} c_{1} -1} \]

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 44

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

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-6) (K[1]+2)}dK[1]\&\right ][-t+c_1] \\ y(t)\to -2 \\ y(t)\to 6 \\ \end{align*}

✓ Sympy. Time used: 0.388 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = - \frac {2 \left (e^{8 C_{1} - 8 t} + 3\right )}{e^{8 C_{1} - 8 t} - 1} \]