Internal problem ID [8268]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 688.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 61
dsolve(diff(y(x),x) = (y(x)+exp((x+1)/(x-1))*x^3+exp((x+1)/(x-1))*x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {{\mathrm e}^{\frac {x +1}{x -1}} x^{2}}{2}+x \,{\mathrm e}^{\frac {x +1}{x -1}}+4 \,{\mathrm e} \expIntegral \left (1, -\frac {2}{x -1}\right )-\frac {3 \,{\mathrm e}^{\frac {x +1}{x -1}}}{2}+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 5.667 (sec). Leaf size: 43
DSolve[y'[x] == (E^((1 + x)/(-1 + x))*x^3 + y[x] + E^((1 + x)/(-1 + x))*x*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan \left (-4 e \text {ExpIntegralEi}\left (\frac {2}{x-1}\right )+\frac {1}{2} e^{\frac {x+1}{x-1}} (x-1) (x+3)+c_1\right ) \\ \end{align*}