89.32.2 problem 2

Internal problem ID [24962]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:45:04 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\begin{align*} y &= c_1 \,x^{{1}/{3}} \\ y &= \frac {x}{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to c_1 \sqrt [3]{x}\\ y(x)&\to \frac {x}{2}+c_1\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 15

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

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