Internal problem ID [8302]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 724.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
\[ \boxed {y^{\prime }+\frac {y^{3}}{\left (-1+\ln \left (x \right ) y-y\right ) x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x) = -y(x)^3/(-1+y(x)*ln(x)-y(x))/x,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-2} x \right )-\ln \left (x \right )+2} \]
✓ Solution by Mathematica
Time used: 12.262 (sec). Leaf size: 422
DSolve[y'[x] == -(y[x]^3/(x*(-1 - y[x] + Log[x]*y[x]))),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {\sqrt [3]{-2} \left (\frac {1-y(x) (\log (x)-4)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\log \left (\frac {2^{2/3} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+2 (-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )-\log \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )+3\right )}{9 \left (\frac {(y(x) (\log (x)-4)-1)^3}{(y(x) (\log (x)-1)-1)^3}+\frac {3 \sqrt [3]{-1} (y(x) (\log (x)-4)-1)}{\left (-\frac {1}{(\log (x)-1)^3}\right )^{4/3} (\log (x)-1)^4 (y(x) (\log (x)-1)-1)}+2\right )}=\frac {1}{9} 2^{2/3} \left (-\frac {1}{(\log (x)-1)^3}\right )^{2/3} \log (x) (\log (x)-1)^2+c_1,y(x)\right ] \]