44.13.17 problem 16(b)

Internal problem ID [9318]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 16(b)
Date solved : Tuesday, September 30, 2025 at 06:16:23 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: 0.012 (sec). Leaf size: 58

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

\begin{align*} y(x)&\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}\int _1^{K[2]}(\sin (K[1])+24)dK[1]dK[2]dK[3]dK[4]+x (x (c_4 x+c_3)+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.041 (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)
 

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