78.16.14 problem 14

Internal problem ID [18393]
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 : 14
Date solved : Tuesday, January 28, 2025 at 11:49:21 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-diff(y(x),x$2)=12*x-2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{1} -5 x^{2}-2 x^{3}+c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]==12*x-2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x^3-5 x^2+c_3 x+c_1 e^x+c_2 \]