Internal problem ID [8757]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 421.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}-2 y y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 32
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)-x = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \frac {-c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 71
DSolve[-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} \left (-x^2+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}