Internal problem ID [6313]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+y^{2}-x y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x)+y(x)^2=x*y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 8.879 (sec). Leaf size: 25
DSolve[x^2*y'[x]+y[x]^2==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \text {ProductLog}\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}