Internal problem ID [8267]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 687.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (y(x)-ln((x+1)/(x-1))*x^3+ln((x+1)/(x-1))*x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}+c_{1}+x -1\right ) x \]
✓ Solution by Mathematica
Time used: 2.442 (sec). Leaf size: 85
DSolve[y'[x] == (-(x^3*Log[(1 + x)/(-1 + x)]) + y[x] + x*Log[(1 + x)/(-1 + x)]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (x+1) (x-1)^{x^2}+x (x+1)^{x^2} (x-1) e^{2 (x+c_1)}}{(x-1)^{x^2} (x+1)-(x-1) (x+1)^{x^2} e^{2 (x+c_1)}} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}