Internal problem ID [9303]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1725 (book 6.134).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x)*(x-y(x))+2*diff(y(x),x)*(diff(y(x),x)+1)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-x c_{2}+c_{2}^{2}+c_{1}}{c_{2}-x} \]
✓ Solution by Mathematica
Time used: 0.761 (sec). Leaf size: 24
DSolve[2*y'[x]*(1 + y'[x]) + (x - y[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-c_1}}{x+c_2}-c_2 \\ \end{align*}