76.4.1 problem 1

Internal problem ID [17395]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 10:04:25 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 43

dsolve((2*x+3)+(2*y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 1-\sqrt {-x^{2}-c_{1} -3 x +1} \\ y &= 1+\sqrt {-x^{2}-c_{1} -3 x +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 51

DSolve[(2*x+3)+(2*y[x]-2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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