Internal problem ID [7834]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 254.
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 {x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve(x*(x*y(x)-2)*diff(y(x),x)+x^2*y(x)^3+x*y(x)^2-2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {1-4 \ln \relax (x )+4 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ y \relax (x ) = \frac {1+\sqrt {1-4 \ln \relax (x )+4 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.819 (sec). Leaf size: 85
DSolve[x*(x*y[x]-2)*y'[x]+x^2*y[x]^3+x*y[x]^2-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{x+\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x (-4 \log (x)+1+4 c_1)}} \\ y(x)\to \frac {2}{x+\left (-\frac {1}{x^3}\right )^{3/2} x^5 \sqrt {x (4 \log (x)-1-4 c_1)}} \\ y(x)\to 0 \\ \end{align*}