78.15.17 problem 19 (b)

Internal problem ID [18302]
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 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 19 (b)
Date solved : Monday, March 31, 2025 at 05:25:09 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = sin(x)+24; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}}{6}+x^{4}+\frac {c_2 \,x^{2}}{2}+\sin \left (x \right )+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 29

ode=D[y[x],{x,4}]==Sin[x]+24; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^4+c_4 x^3+c_3 x^2+\sin (x)+c_2 x+c_1 \]

✓ Sympy. Time used: 0.072 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x) + Derivative(y(x), (x, 4)) - 24,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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