47.1.2 problem 2

Internal problem ID [9722]
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 : 2
Date solved : Tuesday, September 30, 2025 at 06:32:20 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=x*diff(y(x),x)^2-(2*x+3*y(x))*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=x*(D[y[x],x])^2-(2*x+3*y[x])*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**2 - (2*x + 3*y(x))*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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