Internal problem ID [8042]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 464.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}+2 y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 75
dsolve(y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x \\ y \left (x \right ) = i x \\ y \left (x \right ) = 0 \\ y \left (x \right ) = \sqrt {c_{1}^{2}-2 x c_{1}} \\ y \left (x \right ) = \sqrt {c_{1}^{2}+2 x c_{1}} \\ y \left (x \right ) = -\sqrt {c_{1}^{2}-2 x c_{1}} \\ y \left (x \right ) = -\sqrt {c_{1}^{2}+2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.479 (sec). Leaf size: 126
DSolve[-y[x] + 2*x*y'[x] + y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}