Internal problem ID [9018]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 683.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(diff(y(x),x) = y(x)*(-1+ln(x*(x+1))*y(x)*x^4-ln(x*(x+1))*x^3)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{x \left (\left (x \left (x +1\right )\right )^{\frac {x^{3}}{3}} \left (x +1\right )^{\frac {1}{3}} {\mathrm e}^{-\frac {2}{9} x^{3}+\frac {1}{6} x^{2}-\frac {1}{3} x} c_{1} +1\right )} \]
✓ Solution by Mathematica
Time used: 1.1 (sec). Leaf size: 77
DSolve[y'[x] == (y[x]*(-1 - x^3*Log[x*(1 + x)] + x^4*Log[x*(1 + x)]*y[x]))/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {1}{9} x \left (2 x^2+3\right )}}{x \left (e^{\frac {1}{9} x \left (2 x^2+3\right )}+c_1 e^{\frac {x^2}{6}} \sqrt [3]{x+1} (x (x+1))^{\frac {x^3}{3}}\right )} y(x)\to 0 \end{align*}