78.15.17 problem 19 (b)

Internal problem ID [18373]
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 : Tuesday, January 28, 2025 at 11:48:28 AM
CAS classification : [[_high_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)=sin(x)+24,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{3}}{6}+x^{4}+\frac {c_{2} x^{2}}{2}+\sin \left (x \right )+c_3 x +c_4 \]

✓ Solution by Mathematica

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

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

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