78.16.22 problem 22

Internal problem ID [18330]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 22
Date solved : Monday, March 31, 2025 at 05:25:44 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=\frac {1}{x^{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 1/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}}{6}+\frac {c_2 \,x^{2}}{2}+\frac {x \ln \left (x \right )}{2}-\frac {x}{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 33

ode=D[y[x],{x,4}]==1/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_4 x^3+c_3 x^2+\frac {1}{2} x (\log (x)-1)+c_2 x+c_1 \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 4)) - 1/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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