78.16.15 problem 15

Internal problem ID [18394]
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 : 15
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 }&=9 x^{2}-2 x +1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(x),x$3)+diff(y(x),x$2)=9*x^2-2*x+1,y(x), singsol=all)
 

\[ y = \frac {21 x^{2}}{2}-\frac {10 x^{3}}{3}+\frac {3 x^{4}}{4}+{\mathrm e}^{-x} c_{1} +c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 41

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]==9*x^2-2*x+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x^4}{4}-\frac {10 x^3}{3}+\frac {21 x^2}{2}+c_3 x+c_1 e^{-x}+c_2 \]