6.2 problem 2

Internal problem ID [4407]

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]

\[ \boxed {{y^{\prime }}^{2}=\frac {a^{2}}{x^{2}}} \]

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 20

dsolve((diff(y(x),x))^2-a^2/x^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= a \ln \left (x \right )+c_{1} \\ y \left (x \right ) &= -a \ln \left (x \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (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*}