Internal problem ID [15122]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 260.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {\left (1+{y^{\prime }}^{2}\right ) y^{2}-4 y y^{\prime }=4 x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 71
dsolve((1+diff(y(x),x)^2)*y(x)^2-4*y(x)*diff(y(x),x)-4*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \sqrt {x +1} \\ y \left (x \right ) &= 2 \sqrt {x +1} \\ y \left (x \right ) &= \sqrt {-c_{1}^{2}+2 c_{1} x -x^{2}+4 x +4} \\ y \left (x \right ) &= -\sqrt {-x^{2}+\left (2 c_{1} +4\right ) x -c_{1}^{2}+4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.459 (sec). Leaf size: 65
DSolve[(1+y'[x]^2)*y[x]^2-4*y[x]*y'[x]-4*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {-4 x^2-4 (-4+c_1) x+16-c_1{}^2} \\ y(x)\to \frac {1}{2} \sqrt {-4 x^2-4 (-4+c_1) x+16-c_1{}^2} \\ \end{align*}