Internal problem ID [8379]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 799.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+y \,{\mathrm e}^{\frac {x +1}{x -1}} x^{3}\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.073 (sec). Leaf size: 147
dsolve(diff(y(x),x) = y(x)*(-1-x*exp((x+1)/(x-1))+x^2*exp((x+1)/(x-1))*y(x)-x^2*exp((x+1)/(x-1))+x^3*exp((x+1)/(x-1))*y(x))/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {x +1}{x -1}}}{2}} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x +1}{x -1}} x^{2}}{2}} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {x +1}{x -1}}} {\mathrm e}^{-6 \,{\mathrm e} \expIntegral \left (1, -\frac {2}{x -1}\right )}}{x \left (c_{1}+\int -\left (x +1\right ) {\mathrm e}^{\frac {x +1}{x -1}} {\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {x +1}{x -1}}}{2}} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x +1}{x -1}} x^{2}}{2}} {\mathrm e}^{-6 \,{\mathrm e} \expIntegral \left (1, -\frac {2}{x -1}\right )} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {x +1}{x -1}}}d x \right )} \]
✓ Solution by Mathematica
Time used: 1.527 (sec). Leaf size: 53
DSolve[y'[x] == (y[x]*(-1 - E^((1 + x)/(-1 + x))*x - E^((1 + x)/(-1 + x))*x^2 + E^((1 + x)/(-1 + x))*x^2*y[x] + E^((1 + x)/(-1 + x))*x^3*y[x]))/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x+c_1 x \exp \left (\frac {1}{2} e^{\frac {x+1}{x-1}} (x-1) (x+5)-6 e \text {Ei}\left (\frac {2}{x-1}\right )\right )} \\ y(x)\to 0 \\ \end{align*}