Internal problem ID [4478]
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]
\[ \boxed {y^{2}+x y y^{\prime }=-x^{2}-x} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.242 (sec). Leaf size: 60
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 {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*}