54.2.2 problem 2

Internal problem ID [8534]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 2
Date solved : Wednesday, March 05, 2025 at 06:02:53 AM
CAS classification : [_quadrature]

\begin{align*} 6 x {y^{\prime }}^{2}-\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: 0.05 (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: 0.162 (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)
 

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