Internal problem ID [3900]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 3.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {1-x}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 47
dsolve((diff(y(x),x))^2=(1-x)/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x^{2}+x}+\frac {\arcsin \left (2 x -1\right )}{2}+c_{1} \\ y \relax (x ) = -\sqrt {-x^{2}+x}-\frac {\arcsin \left (2 x -1\right )}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 77
DSolve[(y'[x])^2==(1-x)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {-((x-1) x)}-2 \cot ^{-1}\left (\frac {\sqrt {x}+1}{\sqrt {1-x}}\right )+c_1 \\ y(x)\to -\sqrt {-((x-1) x)}+2 \cot ^{-1}\left (\frac {\sqrt {x}+1}{\sqrt {1-x}}\right )+c_1 \\ \end{align*}