Internal problem ID [8265]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 685.
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 (\left (x -1\right ) \left (x +1\right )\right ) x^{3}+7 \ln \left (\left (x -1\right ) \left (x +1\right )\right ) x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.057 (sec). Leaf size: 48
dsolve(diff(y(x),x) = (y(x)+ln((x+1)*(x-1))*x^3+7*ln((x+1)*(x-1))*x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\left (x^{2} \ln \left (\left (x -1\right ) \left (x +1\right )\right )-x^{2}-\ln \left (\left (x -1\right ) \left (x +1\right )\right )+2 c_{1}+1\right ) \sqrt {7}}{2}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 1.688 (sec). Leaf size: 55
DSolve[y'[x] == (x^3*Log[(-1 + x)*(1 + x)] + y[x] + 7*x*Log[(-1 + x)*(1 + x)]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (\frac {1}{2} \sqrt {7} \left (x^2 (\log (x-1)+\log (x+1)-1)-\log (1-x)-\log (x+1)+2 c_1\right )\right )}{\sqrt {7}} \\ \end{align*}