31.6.2 problem 2

Internal problem ID [5751]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 2
Date solved : Sunday, March 30, 2025 at 10:08:05 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\begin{align*} y &= a \ln \left (x \right )+c_1 \\ y &= -a \ln \left (x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

ode=(D[y[x],x])^2-a^2/x^2==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**2/x**2 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} - a \log {\left (x \right )}, \ y{\left (x \right )} = C_{1} + a \log {\left (x \right )}\right ] \]