Internal problem ID [15117]
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: 229.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {-\frac {1}{{y^{\prime }}^{2}}=-x +\frac {y}{y^{\prime }}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(x=y(x)/diff(y(x),x)+1/diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \sqrt {-x} \\ y \left (x \right ) &= 2 \sqrt {-x} \\ y \left (x \right ) &= c_{1} x -\frac {1}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 47
DSolve[x==y[x]/y'[x]+1/y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 i \sqrt {x} \\ y(x)\to 2 i \sqrt {x} \\ \end{align*}