78.16.10 problem 10

Internal problem ID [18389]
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 : 10
Date solved : Tuesday, January 28, 2025 at 11:49:15 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

dsolve(diff(y(x),x$5)-diff(y(x),x$3)=x^2,y(x), singsol=all)
 

\[ y = -\frac {x^{3}}{3}-\frac {x^{5}}{60}+c_{2} {\mathrm e}^{x}+\frac {c_3 \,x^{2}}{2}-{\mathrm e}^{-x} c_{1} +c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 47

DSolve[D[y[x],{x,5}]-D[y[x],{x,3}]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^5}{60}-\frac {x^3}{3}+c_5 x^2+c_4 x+c_1 e^x-c_2 e^{-x}+c_3 \]