Internal problem ID [7718]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 138.
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: 11
dsolve(x^2*diff(y(x),x) - y(x)^2 - x*y(x) - x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (c_{1}+\ln \relax (x )\right ) x \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 13
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 \tan (\log (x)+c_1) \\ \end{align*}