31.6.3 problem 3

Internal problem ID [5752]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:12:46 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=\frac {1-x}{x} \end{align*}

✓ Solution by Maple

Time used: 0.043 (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: 0.178 (sec). Leaf size: 51

DSolve[(D[y[x],x])^2==(1-x)/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arcsin \left (\sqrt {x}\right )-\sqrt {-((x-1) x)}+c_1 \\ y(x)\to \arcsin \left (\sqrt {x}\right )+\sqrt {-((x-1) x)}+c_1 \\ \end{align*}