Internal problem ID [8759]
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]
\[ \boxed {x {y^{\prime }}^{2}-2 y y^{\prime }+2 y=-x} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 44
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 \left (x \right ) &= \left (1-\sqrt {2}\right ) x \\ y \left (x \right ) &= \left (1+\sqrt {2}\right ) x \\ y \left (x \right ) &= \frac {2 c_{1}^{2}+2 c_{1} x +x^{2}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.245 (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*}