58.13.21 problem 21

Internal problem ID [14832]
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 : 21
Date solved : Thursday, October 02, 2025 at 09:55:31 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=0 \\ y^{\prime }\left (2\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 11

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 0; 
ic:=[y(2) = 0, D(y)(2) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{2} \left (x -2\right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 12

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0; 
ic={y[2]==0,Derivative[1][y][2]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (x-2) x^2 \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {y(2): 0, Subs(Derivative(y(x), x), x, 2): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (x - 2\right ) \]