Internal problem ID [15114]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number: 226.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x^{2}}{4} \\ y \left (x \right ) &= c_{1} \left (x +c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 23
DSolve[y[x]==x*y'[x]+y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+c_1) \\ y(x)\to -\frac {x^2}{4} \\ \end{align*}