Internal problem ID [7875]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 295.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{2}+y x -x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.384 (sec). Leaf size: 29
dsolve(x*(y(x)^2+x*y(x)-x^2)*diff(y(x),x)-y(x)^3+x*y(x)^2+x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )} x \]
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 31
DSolve[x*(y[x]^2+x*y[x]-x^2)*y'[x]-y[x]^3+x*y[x]^2+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\frac {x}{y(x)}+\frac {y(x)}{x}+\log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]