78.16.20 problem 20

Internal problem ID [18399]
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 : 20
Date solved : Tuesday, January 28, 2025 at 11:49:28 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-y(x)=1-x^3,y(x), singsol=all)
 

\[ y = x^{3}-1+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

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

\[ y(x)\to x^3+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x)-1 \]