58.13.7 problem 7

Internal problem ID [14818]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:55:18 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=3*x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{{1}/{3}}+c_2 \,x^{2} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=3*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^2+c_1 \sqrt [3]{x} \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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