Internal problem ID [1905]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x+y(x)*diff(y(x),x)=2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\LambertW \left (x c_{1}\right )+1\right )}{\LambertW \left (x c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 33
DSolve[x+y[x]*y'[x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}-1\right )-\frac {1}{\frac {y(x)}{x}-1}=-\log (x)+c_1,y(x)\right ] \]