44.7.1 problem 1

Internal problem ID [7200]
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, February 04, 2025 at 12:47:22 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 45

dsolve((2*x-1)+(3*y(x)+7)*diff(y(x),x)=0,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*}

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 59

DSolve[(2*x-1)+(3*y[x]+7)*D[y[x],x]==0,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*}