Internal problem ID [7709]
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]
Solve \begin {gather*} \boxed {y^{\prime } \left (1+x \right )+y \left (y-x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 41
dsolve((x+1)*diff(y(x),x) + y(x)*(y(x)-x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{x}}{{\mathrm e}^{-1} \expIntegral \left (1, -x -1\right ) x +{\mathrm e}^{-1} \expIntegral \left (1, -x -1\right )-c_{1} x +{\mathrm e}^{x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.358 (sec). Leaf size: 34
DSolve[(x+1)*y'[x]+ y[x]*(y[x]-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-1+e^{-x-1} (x+1) (\operatorname {Ei}(x+1)+e c_1)} \\ y(x)\to 0 \\ \end{align*}