Internal problem ID [7855]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 275.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (x +x^{2}+y^{2}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 30
dsolve((y(x)^2+x^2+x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ c_{1}+\frac {{\mathrm e}^{-2 i y \relax (x )} \left (i x +y \relax (x )\right )}{2 i y \relax (x )+2 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 18
DSolve[(y[x]^2+x^2+x)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [y(x)-\operatorname {ArcTan}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]