Internal problem ID [8476]
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]
\[ \boxed {x^{2} \left (y^{\prime }+y^{2}\right )+4 y x=-2} \]
✓ 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)
\[ y \left (x \right ) = -\frac {2 c_{1} -x}{x \left (-x +c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.151 (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*}