Internal problem ID [9023]
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]
\[ \boxed {y^{\prime }-\frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
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)
\[ y \left (x \right ) = \tan \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 5.536 (sec). Leaf size: 45
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]
\[ y(x)\to x \tan \left (-4 e \operatorname {ExpIntegralEi}\left (\frac {2}{x-1}\right )+\frac {1}{2} e^{\frac {x+1}{x-1}} \left (x^2+2 x-3\right )+c_1\right ) \]