78.16.23 problem 23

Internal problem ID [18402]
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 : 23
Date solved : Tuesday, January 28, 2025 at 11:49:29 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }&=1+x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 55

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

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

✓ Solution by Mathematica

Time used: 0.382 (sec). Leaf size: 79

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

\[ y(x)\to \frac {1}{2} \left (x (x+4)+\left (c_1-\sqrt {3} c_2\right ) e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+\left (\sqrt {3} c_1+c_2\right ) e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )\right )+c_3 \]