44.4.48 problem 36

Internal problem ID [7061]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 36
Date solved : Wednesday, March 05, 2025 at 04:04:52 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 24

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

\[ y = \frac {-3-2 \,{\mathrm e}^{5 x} c_{1}}{{\mathrm e}^{5 x} c_{1} -1} \]

✓ Mathematica. Time used: 0.475 (sec). Leaf size: 40

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

\begin{align*} y(x)\to \frac {-3-2 e^{5 (x+c_1)}}{-1+e^{5 (x+c_1)}} \\ y(x)\to -2 \\ y(x)\to 3 \\ \end{align*}

✓ Sympy. Time used: 0.376 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {3 e^{5 C_{1} - 5 x} + 2}{e^{5 C_{1} - 5 x} - 1} \]