Internal problem ID [7717]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 137.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-y^{2}-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x) - y(x)^2 - x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{\ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 21
DSolve[x^2*y'[x] - y[x]^2 - x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}