Internal problem ID [4805]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\left (-1-2 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+2 \sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )\right ) x}+c_{2} {\mathrm e}^{-2 \left (\sqrt {3}\, \cos \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+\sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )+\frac {1}{2}\right ) x}+c_{3} {\mathrm e}^{\left (4 \sin \left (\frac {\arctan \left (\frac {\sqrt {55}}{3}\right )}{3}+\frac {\pi }{6}\right )-1\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 87
DSolve[y'''[x]+3*y''[x]-9*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-9 \text {$\#$1}-5\&,1\right ]\right ) \]