78.16.11 problem 11

Internal problem ID [18390]
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 : 11
Date solved : Tuesday, January 28, 2025 at 11:49:16 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\left (6\right )}-y&=x^{10} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 79

dsolve(diff(y(x),x$6)-y(x)=x^(10),y(x), singsol=all)
 

\[ y = -\left (\left (-{\mathrm e}^{\frac {x}{2}} c_3 -{\mathrm e}^{\frac {3 x}{2}} c_5 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left (-{\mathrm e}^{\frac {x}{2}} c_4 -{\mathrm e}^{\frac {3 x}{2}} c_6 \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )-c_{1} {\mathrm e}^{2 x}+\left (x^{10}+151200 x^{4}\right ) {\mathrm e}^{x}-c_{2} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 86

DSolve[D[y[x],{x,6}]-y[x]==x^10,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x^{10}-151200 x^4+c_1 e^x+c_4 e^{-x}+e^{-x/2} \left (c_2 e^x+c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{-x/2} \left (c_6 e^x+c_5\right ) \sin \left (\frac {\sqrt {3} x}{2}\right ) \]