Internal problem ID [7716]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 136.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+y^{2}+y x +x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x) + y(x)^2 + x*y(x) + x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (\ln \relax (x )+c_{1}-1\right )}{c_{1}+\ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 25
DSolve[x^2*y'[x] + y[x]^2 + x*y[x] + x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-1+\frac {1}{\log (x)-c_1}\right ) \\ y(x)\to -x \\ \end{align*}