Internal problem ID [7883]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 303.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (y x -1\right )^{2} x y^{\prime }+\left (y^{2} x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.484 (sec). Leaf size: 34
dsolve((x*y(x)-1)^2*x*diff(y(x),x)+(x^2*y(x)^2+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 25
DSolve[(x*y[x]-1)^2*x*y'[x]+(x^2*y[x]^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ] \]