Internal problem ID [3917]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 20.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y-2 y^{\prime } x -x \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 49
dsolve(y(x)-2*x*diff(y(x),x)=(x*(diff(y(x),x))^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = \left (\frac {c_{1}}{x}+\frac {2 \sqrt {c_{1} x}}{x}\right ) x \\ y \relax (x ) = \left (\frac {c_{1}}{x}-\frac {2 \sqrt {c_{1} x}}{x}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 63
DSolve[y[x]-2*x*y'[x]==(x*(y'[x])^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{c_1}-2 e^{\frac {c_1}{2}} \sqrt {x} \\ y(x)\to 2 e^{-\frac {c_1}{2}} \sqrt {x}+e^{-c_1} \\ y(x)\to 0 \\ y(x)\to -x \\ \end{align*}