38.4.42 problem 24

Internal problem ID [8341]
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 : 24
Date solved : Tuesday, September 30, 2025 at 05:29:23 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=10+3 y-y^{2} \end{align*}

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

ode:=diff(y(x),x) = 10+3*y(x)-y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 \,{\mathrm e}^{7 x} c_1 +2}{-1+{\mathrm e}^{7 x} c_1} \]

✓ Mathematica. Time used: 0.12 (sec). Leaf size: 44

ode=D[y[x],x]==10+3*y[x]-y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-5) (K[1]+2)}dK[1]\&\right ][-x+c_1]\\ y(x)&\to -2\\ y(x)&\to 5 \end{align*}

✓ Sympy. Time used: 0.235 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 - 3*y(x) + Derivative(y(x), x) - 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {2 e^{7 C_{1} - 7 x} + 5}{e^{7 C_{1} - 7 x} - 1} \]