Internal problem ID [4408]
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]
\[ \boxed {{y^{\prime }}^{2}=\frac {1-x}{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve((diff(y(x),x))^2=(1-x)/x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-x \left (x -1\right )}+\frac {\arcsin \left (2 x -1\right )}{2}+c_{1} \\ y \left (x \right ) &= -\sqrt {-x \left (x -1\right )}-\frac {\arcsin \left (2 x -1\right )}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 81
DSolve[(y'[x])^2==(1-x)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \arctan \left (\frac {\sqrt {1-x}}{\sqrt {x}+1}\right )+\sqrt {-((x-1) x)}+c_1 \\ y(x)\to 2 \arctan \left (\frac {\sqrt {1-x}}{\sqrt {x}+1}\right )-\sqrt {-((x-1) x)}+c_1 \\ \end{align*}