Internal problem ID [3915]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 18.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{\prime } y-x -y^{2}+y^{2} \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.15 (sec). Leaf size: 65
dsolve(y(x)*diff(y(x),x)=x+(y(x)^2-y(x)^2*(diff(y(x),x))^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-4 x -1}}{2} \\ y \relax (x ) = \frac {\sqrt {-4 x -1}}{2} \\ y \relax (x ) = \sqrt {c_{1}^{2}-2 c_{1} x +x^{2}-c_{1}} \\ y \relax (x ) = -\sqrt {c_{1}^{2}-2 c_{1} x +x^{2}-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 67
DSolve[y[x]*y'[x]==x+(y[x]^2-y[x]^2*(y'[x])^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {-1+4 \left ((x-1) x-4 c_1 x+4 c_1{}^2\right )} \\ y(x)\to \frac {1}{2} \sqrt {-1+4 \left ((x-1) x-4 c_1 x+4 c_1{}^2\right )} \\ \end{align*}