23.2.141 problem 144

Internal problem ID [5496]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 144
Date solved : Tuesday, September 30, 2025 at 12:45:34 PM
CAS classification : [_quadrature]

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

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

ode:=x^2*diff(y(x),x)^2 = a^2; 
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: 0.002 (sec). Leaf size: 24

ode=x^2 (D[y[x],x])^2==a^2; 
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: 0.115 (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)
 

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