78.6.2 problem 2.a

Internal problem ID [21065]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 7, Nonlinear systems. Problems section 7.11
Problem number : 2.a
Date solved : Thursday, October 02, 2025 at 07:02:02 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-6 y-16 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(y(x),x) = y(x)^2-6*y(x)-16; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-8-2 \,{\mathrm e}^{10 x} c_1}{{\mathrm e}^{10 x} c_1 -1} \]

✓ Mathematica. Time used: 0.378 (sec). Leaf size: 39

ode=D[y[x],x]==y[x]^2-6*y[x]-16; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2 \left (4+e^{10 (x+c_1)}\right )}{-1+e^{10 (x+c_1)}}\\ y(x)&\to -2\\ y(x)&\to 8 \end{align*}

✓ Sympy. Time used: 0.237 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 + 6*y(x) + Derivative(y(x), x) + 16,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 \left (4 e^{10 C_{1} - 10 x} + 1\right )}{e^{10 C_{1} - 10 x} - 1} \]