29.20.23 problem 570

Internal problem ID [5164]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 570
Date solved : Monday, January 27, 2025 at 10:16:43 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \end{align*}

✓ Solution by Maple

Time used: 5.957 (sec). Leaf size: 72

dsolve(x*(3-x*y(x))*diff(y(x),x) = y(x)*(x*y(x)-1),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {3 \operatorname {LambertW}\left (\frac {\left (-x^{2}\right )^{{1}/{3}} c_{1}}{3}\right )}{x} \\ y \left (x \right ) &= -\frac {3 \operatorname {LambertW}\left (-\frac {\left (-x^{2}\right )^{{1}/{3}} c_{1} \left (1+i \sqrt {3}\right )}{6}\right )}{x} \\ y \left (x \right ) &= -\frac {3 \operatorname {LambertW}\left (\frac {\left (-x^{2}\right )^{{1}/{3}} c_{1} \left (i \sqrt {3}-1\right )}{6}\right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 9.052 (sec). Leaf size: 35

DSolve[x(3-x y[x])D[y[x],x]==y[x](x y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 W\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^{2/3}\right )}{x} \\ y(x)\to 0 \\ \end{align*}