73.13.27 problem 20.4 (c)

Internal problem ID [15334]
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 : 20.4 (c)
Date solved : Monday, March 31, 2025 at 01:34:40 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=x^3*diff(diff(diff(y(x),x),x),x)-5*x^2*diff(diff(y(x),x),x)+14*x*diff(y(x),x)-18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (\ln \left (x \right ) c_3 x +c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 22

ode=x^3*D[y[x],{x,3}]-5*x^2*D[y[x],{x,2}]+14*x*D[y[x],x]-18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (c_2 x+c_3 x \log (x)+c_1) \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 5*x**2*Derivative(y(x), (x, 2)) + 14*x*Derivative(y(x), x) - 18*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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