38.7.1 problem 1

Internal problem ID [8486]
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 2.4 Exact equations. Exercises 2.4 at page 71
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 05:38:05 PM
CAS classification : [_separable]

\begin{align*} 2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 45

ode:=2*x-1+(3*y(x)+7)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {7}{3}-\frac {\sqrt {-6 x^{2}-6 c_1 +6 x +49}}{3} \\ y &= -\frac {7}{3}+\frac {\sqrt {-6 x^{2}-6 c_1 +6 x +49}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 59

ode=(2*x-1)+(3*y[x]+7)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} \left (-7-\sqrt {-6 x^2+6 x+49+6 c_1}\right )\\ y(x)&\to \frac {1}{3} \left (-7+\sqrt {-6 x^2+6 x+49+6 c_1}\right ) \end{align*}

✓ Sympy. Time used: 0.280 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (3*y(x) + 7)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} - 6 x^{2} + 6 x}}{3} - \frac {7}{3}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} - 6 x^{2} + 6 x}}{3} - \frac {7}{3}\right ] \]