35.5.15 problem 26

Internal problem ID [6149]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 26
Date solved : Monday, January 27, 2025 at 01:38:27 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 105

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-9*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\left (-1-2 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+2 \sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )\right ) x}+c_2 \,{\mathrm e}^{-2 x \left (\sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+\sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+\frac {1}{2}\right )}+c_3 \,{\mathrm e}^{\left (4 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )-1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 87

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-9*D[y[x],x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,1\right ]\right ) \]