47.1.1 problem 1

Internal problem ID [9721]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 06:32:20 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\begin{align*} y &= c_1 x \\ y &= \frac {c_1}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {c_1}{x}\\ y(x)&\to c_1 x\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 10

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

\[ \left [ y{\left (x \right )} = C_{1} x, \ y{\left (x \right )} = \frac {C_{1}}{x}\right ] \]