Internal problem ID [3887]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 4
Problem number: 7.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (y^{3} x^{3}+x^{2} y^{2}+y x +1\right ) y+\left (y^{3} x^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 42
dsolve((x^3*y(x)^3+x^2*y(x)^2+x*y(x)+1)*y(x)+(x^3*y(x)^3-x^2*y(x)^2-x*y(x)+1)*x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{x} \\ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 35
DSolve[(x^3*y[x]^3+x^2*y[x]^2+x*y[x]+1)*y[x]+(x^3*y[x]^3-x^2*y[x]^2-x*y[x]+1)*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x} \\ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ] \\ \end{align*}