85.68.4 problem 6

Internal problem ID [22915]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 217
Problem number : 6
Date solved : Friday, October 03, 2025 at 08:03:35 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

ode:=diff(diff(diff(y(x),x),x),x) = 24*(x+y(x))/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x +c_1 \,x^{4}+\frac {c_2 \cos \left (\frac {\sqrt {23}\, \ln \left (x \right )}{2}\right )}{\sqrt {x}}+\frac {c_3 \sin \left (\frac {\sqrt {23}\, \ln \left (x \right )}{2}\right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 56

ode=D[y[x],{x,3}]==24*(x+y[x])/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^{3/2} \left (-1+c_3 x^3\right )+c_2 \cos \left (\frac {1}{2} \sqrt {23} \log (x)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {23} \log (x)\right )}{\sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 3)) - (24*x + 24*y(x))/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x^{\frac {9}{2}} + C_{2} \sin {\left (\frac {\sqrt {23} \log {\left (x \right )}}{2} \right )} + C_{3} \cos {\left (\frac {\sqrt {23} \log {\left (x \right )}}{2} \right )} - x^{\frac {3}{2}}}{\sqrt {x}} \]