Internal problem ID [8580]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 1000.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y x^{2}+x^{3}+\ln \relax (x ) y x -y^{2}-y x}{x^{2} \left (\ln \relax (x )+x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x) = 1/x^2*(2*x^2*y(x)+x^3+y(x)*ln(x)*x-y(x)^2-x*y(x))/(x+ln(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (c_{1} x -1\right )}{c_{1} \ln \relax (x )+1} \]
✓ Solution by Mathematica
Time used: 1.408 (sec). Leaf size: 27
DSolve[y'[x] == (x^3 - x*y[x] + 2*x^2*y[x] + x*Log[x]*y[x] - y[x]^2)/(x^2*(x + Log[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (x-c_1)}{\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}