Internal problem ID [3970]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2}+y^{2}+x +x y y^{\prime }=0} \end {gather*}
✓ 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 \relax (x ) = -\frac {\sqrt {-18 x^{4}-24 x^{3}+36 c_{1}}}{6 x} \\ y \relax (x ) = \frac {\sqrt {-18 x^{4}-24 x^{3}+36 c_{1}}}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.231 (sec). Leaf size: 56
DSolve[(x^2+y[x]^2+x)+(x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-\frac {1}{6} x^3 (3 x+4)+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {1}{6} x^3 (3 x+4)+c_1}}{x} \\ \end{align*}