Internal problem ID [3312]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 570.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (3-y x \right ) y^{\prime }-\left (y x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.072 (sec). Leaf size: 74
dsolve(x*(3-x*y(x))*diff(y(x),x) = y(x)*(x*y(x)-1),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {3 \LambertW \left (\frac {2 \left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} c_{1}}{3}\right )}{x} \\ y \relax (x ) = -\frac {3 \LambertW \left (\frac {\left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} c_{1} \left (-1+i \sqrt {3}\right )}{3}\right )}{x} \\ y \relax (x ) = -\frac {3 \LambertW \left (-\frac {\left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} c_{1} \left (1+i \sqrt {3}\right )}{3}\right )}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 30.286 (sec). Leaf size: 35
DSolve[x(3-x y[x])y'[x]==y[x](x y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 \text {ProductLog}\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^{2/3}\right )}{x} \\ y(x)\to 0 \\ \end{align*}