Internal problem ID [3443]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 705.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (-y x +1\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (1+y x \right ) \left (1+x^{2} y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.069 (sec). Leaf size: 42
dsolve(x*(1-x*y(x))*(1-x^2*y(x)^2)*diff(y(x),x)+(1+x*y(x))*(1+x^2*y(x)^2)*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{x} \\ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (-2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )-{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 35
DSolve[x(1-x y[x])(1-x^2 y[x]^2)y'[x]+(1+x y[x])(1+x^2 y[x]^2)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*}