32.4.11 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.3, page 90

Internal problem ID [5822]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.3, page 90
Date solved : Monday, January 27, 2025 at 01:20:03 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 49

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

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-18 x^{4}-24 x^{3}+36 c_{1}}}{6 x} \\ y \left (x \right ) &= \frac {\sqrt {-18 x^{4}-24 x^{3}+36 c_{1}}}{6 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 60

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

\begin{align*} y(x)\to -\frac {\sqrt {-\frac {x^4}{2}-\frac {2 x^3}{3}+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {x^4}{2}-\frac {2 x^3}{3}+c_1}}{x} \\ \end{align*}