Internal problem ID [8267]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 689.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Riccati]
\[ \boxed {y^{\prime }-\frac {y x -y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x) = (x*y(x)-y(x)-exp(x+1)*x^3+exp(x+1)*x*y(x)^2)/(x-1)/x,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left ({\mathrm e}^{x +1}-{\mathrm e}^{2} \operatorname {Ei}_{1}\left (1-x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.891 (sec). Leaf size: 37
DSolve[y'[x] == (-(E^(1 + x)*x^3) - y[x] + x*y[x] + E^(1 + x)*x*y[x]^2)/((-1 + x)*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \tanh \left (e^2 \operatorname {ExpIntegralEi}(x-1)+e^{x+1}+c_1\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}