Internal problem ID [8017]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 437.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Clairaut]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-\left (2 y x +a \right ) y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.257 (sec). Leaf size: 36
dsolve(x^2*diff(y(x),x)^2-(2*x*y(x)+a)*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {a}{4 x} \\ y \relax (x ) = c_{1} x -\sqrt {c_{1} a} \\ y \relax (x ) = c_{1} x +\sqrt {c_{1} a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.362 (sec). Leaf size: 64
DSolve[y[x]^2 - (a + 2*x*y[x])*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to \frac {x+2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{4 x} \\ \end{align*}