Internal problem ID [8276]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 696.
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 (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.075 (sec). Leaf size: 32
dsolve(diff(y(x),x) = (y(x)*ln(x-1)+exp(x+1)*x^3+7*exp(x+1)*x*y(x)^2)/ln(x-1)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\left ({\mathrm e} \left (\int \frac {{\mathrm e}^{x} x}{\ln \left (x -1\right )}d x \right )+c_{1}\right ) \sqrt {7}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 1.365 (sec). Leaf size: 45
DSolve[y'[x] == (E^(1 + x)*x^3 + Log[-1 + x]*y[x] + 7*E^(1 + x)*x*y[x]^2)/(x*Log[-1 + x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (\sqrt {7} \left (\int _1^x\frac {e^{K[1]+1} K[1]}{\log (K[1]-1)}dK[1]+c_1\right )\right )}{\sqrt {7}} \\ \end{align*}