67.13.1 problem 20.1 (a)

Internal problem ID [16666]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.1 (a)
Date solved : Thursday, October 02, 2025 at 01:37:26 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (c_1 \,x^{2}+c_2 \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \left (c_2 x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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