Internal problem ID [3951]
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]
\[ \boxed {x \left (1-y x \right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+x^{2} y^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = -\frac {1}{x} y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )-{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} c_{1} +2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.342 (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*}