15.19.1 problem 1

Internal problem ID [3285]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 1
Date solved : Sunday, March 30, 2025 at 01:31:24 AM
CAS classification : [_separable]

\begin{align*} 4 y^{2}&={y^{\prime }}^{2} x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=4*y(x)^2 = diff(y(x),x)^2*x^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,x^{2} \\ y &= \frac {c_1}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 26

ode=4*y[x]^2==D[y[x],x]^2*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {c_1}{x^2} \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*Derivative(y(x), x)**2 + 4*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} x^{2}, \ y{\left (x \right )} = \frac {C_{1}}{x^{2}}\right ] \]