Internal problem ID [3385]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 646.
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: 0.016 (sec). Leaf size: 22
dsolve(x*(x^2-x*y(x)+y(x)^2)*diff(y(x),x)+(x^2+x*y(x)+y(x)^2)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (\ln \left (\tan \left (\textit {\_Z} \right )\right )-\textit {\_Z} +2 \ln \relax (x )+2 c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 28
DSolve[x(x^2-x y[x]+y[x]^2)y'[x]+(x^2+x y[x]+y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]