Internal problem ID [4187]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 2, Equations of the first order and degree. page 20
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {a x y^{\prime }+2 y-x y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 40
dsolve(a*x*diff(y(x),x)+2*y(x)=x*y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {a \LambertW \left (-\frac {x^{-\frac {2}{a}} {\mathrm e}^{-\frac {2 c_{1}}{a}}}{a}\right )+2 \ln \relax (x )+2 c_{1}}{a}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[a*x*y'[x]+2*y[x]==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -a \text {ProductLog}\left (-\frac {e^{\frac {c_1}{a}} x^{-2/a}}{a}\right ) \\ \end{align*}