Internal problem ID [8753]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 417.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {x {y^{\prime }}^{2}-y y^{\prime }=-a} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 33
dsolve(x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -2 \sqrt {a x} y \left (x \right ) = 2 \sqrt {a x} y \left (x \right ) = x c_{1} +\frac {a}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 53
DSolve[a - y[x]*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a}{c_1}+c_1 x y(x)\to \text {Indeterminate} y(x)\to -2 \sqrt {a} \sqrt {x} y(x)\to 2 \sqrt {a} \sqrt {x} \end{align*}