Internal problem ID [1911]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(y(x)*(x^2-x*y(x)+y(x)^2)+x*diff(y(x),x)*(x^2+x*y(x)+y(x)^2)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (\textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 26
DSolve[y[x]*(x^2-x*y[x]+y[x]^2)+x*y'[x]*(x^2+x*y[x]+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {y(x)}{x}\right )+\log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]