78.16.21 problem 21

Internal problem ID [18400]
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 : 21
Date solved : Tuesday, January 28, 2025 at 11:49:28 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-\frac {y^{\prime }}{4}&=x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x$3)-1/4*diff(y(x),x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]-1/4*D[y[x],x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x^2+2 c_1 e^{x/2}-2 c_2 e^{-x/2}+c_3 \]