73.10.10 problem 15.3

Internal problem ID [15226]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.3
Date solved : Thursday, March 13, 2025 at 05:50:00 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*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 16

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

\[ y(x)\to x^2 (c_2 x+c_1) \]

✓ Sympy. Time used: 0.158 (sec). Leaf size: 10

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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

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