Internal problem ID [3901]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\frac {2 x y^{\prime }}{y}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 45
dsolve((diff(y(x),x))^2+2*x/y(x)*diff(y(x),x)-1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -i x \\ y \relax (x ) = i x \\ y \relax (x ) = -\frac {2 \sqrt {c_{1} x +1}}{c_{1}} \\ y \relax (x ) = \frac {2 \sqrt {c_{1} x +1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 103
DSolve[(y'[x])^2+2*x/y[x]*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ \end{align*}