47.1.3 problem 3

Internal problem ID [9723]
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 : 3
Date solved : Tuesday, September 30, 2025 at 06:32:21 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2}&=0 \end{align*}

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

ode:=x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)+6*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,x^{3} \\ y &= c_1 \,x^{2} \\ \end{align*}

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 26

ode=x^2*(D[y[x],x])^2-5*x*y[x]*D[y[x],x]+6*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x^2\\ y(x)&\to c_1 x^3\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 - 5*x*y(x)*Derivative(y(x), x) + 6*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} x^{3}, \ y{\left (x \right )} = C_{1} x^{2}\right ] \]