Internal problem ID [7720]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 140.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*(diff(y(x),x)+y(x)^2) + 4*x*y(x) + 2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-x +2 c_{1}}{x \left (c_{1}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.285 (sec). Leaf size: 26
DSolve[x^2*(y'[x]+y[x]^2) + 4*x*y[x] + 2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{x}+\frac {1}{x+c_1} \\ y(x)\to -\frac {2}{x} \\ \end{align*}