78.15.13 problem 13

Internal problem ID [18369]
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 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 11:48:27 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \]