73.13.31 problem 20.4 (g)

Internal problem ID [15338]
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 (g)
Date solved : Monday, March 31, 2025 at 01:34:44 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = x \left (c_1 +c_2 \ln \left (x \right )+c_3 \ln \left (x \right )^{2}+c_4 \ln \left (x \right )^{3}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 29

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

\[ y(x)\to x \left (c_4 \log ^3(x)+c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} \log {\left (x \right )} + C_{3} \log {\left (x \right )}^{2} + C_{4} \log {\left (x \right )}^{3}\right ) \]