Internal problem ID [8003]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 423.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-2 y y^{\prime }+2 y+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 36
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+2*y(x)+x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (\frac {\left (x +c_{1}\right )^{2}}{c_{1}^{2}}+1\right ) x}{-\frac {2 \left (x +c_{1}\right )}{c_{1}}+2} \\ y \relax (x ) = x c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 78
DSolve[x + 2*y[x] - 2*y[x]*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{-c_1} x^2+x-e^{c_1} \\ y(x)\to -e^{c_1} x^2+x-\frac {e^{-c_1}}{2} \\ y(x)\to x-\sqrt {2} x \\ y(x)\to \left (1+\sqrt {2}\right ) x \\ \end{align*}