Internal problem ID [3899]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {a^{2}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
dsolve((diff(y(x),x))^2-a^2/x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = a \ln \relax (x )+c_{1} \\ y \relax (x ) = -a \ln \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[(y'[x])^2-a^2/x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -a \log (x)+c_1 \\ y(x)\to a \log (x)+c_1 \\ \end{align*}