76.4.4 problem 4

Internal problem ID [17398]
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 : 4
Date solved : Tuesday, January 28, 2025 at 10:04:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\begin{align*} y &= -\frac {1}{x} \\ y &= \frac {-c_{1} -1}{x} \\ y &= \frac {c_{1} -1}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}