Internal problem ID [8465]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 129.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {\left (x +1\right ) y^{\prime }+y \left (-x +y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve((x+1)*diff(y(x),x) + y(x)*(y(x)-x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x}}{{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (-x -1\right ) x +{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (-x -1\right )-x c_{1} +{\mathrm e}^{x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.333 (sec). Leaf size: 42
DSolve[(x+1)*y'[x]+ y[x]*(y[x]-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{x+1}}{-(x+1) \operatorname {ExpIntegralEi}(x+1)+e \left (e^x-c_1 (x+1)\right )} y(x)\to 0 \end{align*}