78.16.22 problem 22

Internal problem ID [18401]
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 : Tuesday, January 28, 2025 at 11:49:28 AM
CAS classification : [[_high_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

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

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

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