Internal problem ID [13314]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.4 (b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+216 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+216*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-6 x}+c_{2} {\mathrm e}^{3 x} \sin \left (3 \sqrt {3}\, x \right )+c_{3} {\mathrm e}^{3 x} \cos \left (3 \sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 48
DSolve[y'''[x]+216*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-6 x} \left (c_3 e^{9 x} \cos \left (3 \sqrt {3} x\right )+c_2 e^{9 x} \sin \left (3 \sqrt {3} x\right )+c_1\right ) \]