Internal problem ID [4297]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 170
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {\left (i \sqrt {3}\, \left (-3+i \sqrt {55}\right )^{\frac {2}{3}}-4 i \sqrt {3}+\left (-3+i \sqrt {55}\right )^{\frac {2}{3}}+2 \left (-3+i \sqrt {55}\right )^{\frac {1}{3}}+4\right ) x}{2 \left (-3+i \sqrt {55}\right )^{\frac {1}{3}}}}+c_{2} {\mathrm e}^{\frac {\left (i \sqrt {3}\, \left (-3+i \sqrt {55}\right )^{\frac {2}{3}}-4 i \sqrt {3}-\left (-3+i \sqrt {55}\right )^{\frac {2}{3}}-2 \left (-3+i \sqrt {55}\right )^{\frac {1}{3}}-4\right ) x}{2 \left (-3+i \sqrt {55}\right )^{\frac {1}{3}}}}+c_{3} {\mathrm e}^{\frac {\left (\left (-3+i \sqrt {55}\right )^{\frac {2}{3}}-\left (-3+i \sqrt {55}\right )^{\frac {1}{3}}+4\right ) x}{\left (-3+i \sqrt {55}\right )^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 87
DSolve[y'''[x]+3*y''[x]-9*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}