Internal problem ID [3386]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 647.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (x^{2}-y x -y^{2}\right ) y^{\prime }-\left (x^{2}+y x -y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 29
dsolve(x*(x^2-x*y(x)-y(x)^2)*diff(y(x),x) = (x^2+x*y(x)-y(x)^2)*y(x),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(x^2-x y[x]-y[x]^2)y'[x]==(x^2+x y[x]-y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {x}{y(x)}+\frac {y(x)}{x}+\log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]