60.2.148 problem 724

Internal problem ID [10735]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 724
Date solved : Monday, January 27, 2025 at 09:36:38 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 18

dsolve(diff(y(x),x) = -y(x)^3/(-1+y(x)*ln(x)-y(x))/x,y(x), singsol=all)
 

\[ y = \frac {1}{-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-2} x \right )+\ln \left (x \right )-2} \]

✓ Solution by Mathematica

Time used: 0.327 (sec). Leaf size: 108

DSolve[D[y[x],x] == -(y[x]^3/(x*(-1 - y[x] + Log[x]*y[x]))),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {1-(\log (x)-4) y(x)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) ((\log (x)-1) y(x)-1)}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {1}{9} 2^{2/3} \left (-\frac {1}{(\log (x)-1)^3}\right )^{2/3} \log (x) (\log (x)-1)^2+c_1,y(x)\right ] \]