Internal problem ID [7840]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 260.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {\left (2 y x^{2}+x \right ) y^{\prime }-y^{3} x^{2}+2 x y^{2}+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 59
dsolve((2*x^2*y(x)+x)*diff(y(x),x)-x^2*y(x)^3+2*x*y(x)^2+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2+\sqrt {4-2 \ln \relax (x )+2 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ y \relax (x ) = -\frac {2+\sqrt {4-2 \ln \relax (x )+2 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.724 (sec). Leaf size: 78
DSolve[(2*x^2*y[x]+x)*y'[x]-x^2*y[x]^3+2*x*y[x]^2+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-2 x+\sqrt {\frac {1}{x^3}} x^2 \sqrt {x (-2 \log (x)+4+c_1)}} \\ y(x)\to -\frac {1}{2 x+\sqrt {\frac {1}{x^3}} x^2 \sqrt {x (-2 \log (x)+4+c_1)}} \\ y(x)\to 0 \\ \end{align*}