78.16.24 problem 24

Internal problem ID [18403]
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 : 24
Date solved : Tuesday, January 28, 2025 at 11:49:29 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

\[ y = \frac {x^{3}}{12}-\frac {x^{2}}{8}+\frac {{\mathrm e}^{-2 x} c_{1}}{4}+c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 37

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

\[ y(x)\to \frac {x^3}{12}-\frac {x^2}{8}+c_3 x+\frac {1}{4} c_1 e^{-2 x}+c_2 \]