73.13.32 problem 20.4 (h)

Internal problem ID [15339]
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 (h)
Date solved : Monday, March 31, 2025 at 01:34:45 PM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+7*x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{x}+c_2 x +c_3 \sin \left (\ln \left (x \right )\right )+c_4 \cos \left (\ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 28

ode=x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+7*x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x+\frac {c_3}{x}+c_2 \cos (\log (x))+c_4 \sin (\log (x)) \]

✓ Sympy. Time used: 0.256 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 6*x**3*Derivative(y(x), (x, 3)) + 7*x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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