Internal problem ID [7852]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 272.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{2}+x^{2}\right ) y^{\prime }-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.138 (sec). Leaf size: 43
dsolve((y(x)^2+x^2)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {2 \sqrt {3}\, \RootOf \left (2 \sqrt {3}\, {\mathrm e}^{\frac {2 \sqrt {3}\, \textit {\_Z}}{3}} {\mathrm e}^{-c_{1}}-\sqrt {3}\, x +3 \tan \left (\textit {\_Z} \right ) x \right )}{3}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 42
DSolve[(y[x]^2+x^2)*y'[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\frac {2 \operatorname {ArcTan}\left (\frac {\frac {2 y(x)}{x}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]