Internal problem ID [8275]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 695.
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 )+x^{4}+x^{3}+y^{2} x^{2}+y^{2} x}{\ln \left (x -1\right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (y(x)*ln(x-1)+x^4+x^3+x^2*y(x)^2+x*y(x)^2)/ln(x-1)/x,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (-\expIntegral \left (1, -3 \ln \left (x -1\right )\right )-3 \expIntegral \left (1, -2 \ln \left (x -1\right )\right )-2 \expIntegral \left (1, -\ln \left (x -1\right )\right )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.903 (sec). Leaf size: 33
DSolve[y'[x] == (x^3 + x^4 + Log[-1 + x]*y[x] + x*y[x]^2 + x^2*y[x]^2)/(x*Log[-1 + x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (3 \text {ExpIntegralEi}(2 \log (x-1))+\text {ExpIntegralEi}(3 \log (x-1))+2 \text {LogIntegral}(x-1)+c_1) \\ \end{align*}