64.13.3 problem 3

Internal problem ID [13462]
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 : 3
Date solved : Monday, March 31, 2025 at 07:58:35 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = \sqrt {x}\, \left (c_1 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

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

\[ y(x)\to \sqrt {x} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 12

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

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