68.15.64 problem 64 (d)

Internal problem ID [17790]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 64 (d)
Date solved : Thursday, October 02, 2025 at 02:28:17 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 39

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+27*x^2*diff(diff(y(x),x),x)+35*x*diff(y(x),x)+45*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 44

ode=x^4*D[y[x],{x,4}]+8*x^3*D[y[x],{x,3}]+27*x^2*D[y[x],{x,2}]+35*x*D[y[x],x]+45*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 \cos (2 \log (x))+c_3 x \cos (3 \log (x))+c_1 \sin (2 \log (x))+c_4 x \sin (3 \log (x))}{x} \end{align*}

✓ Sympy. Time used: 0.225 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 8*x**3*Derivative(y(x), (x, 3)) + 27*x**2*Derivative(y(x), (x, 2)) + 35*x*Derivative(y(x), x) + 45*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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