78.16.19 problem 19

Internal problem ID [18398]
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 : 19
Date solved : Tuesday, January 28, 2025 at 11:49:27 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-8 y&=16 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

dsolve(diff(y(x),x$3)-8*y(x)=16*x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 50

DSolve[D[y[x],{x,3}]-8*y[x]==16*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (-2 e^x x^2+c_1 e^{3 x}+c_2 \cos \left (\sqrt {3} x\right )+c_3 \sin \left (\sqrt {3} x\right )\right ) \]