Internal problem ID [13313]
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 (a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$3)-8*y(x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_{3} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[y'''[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_1 e^{3 x}+c_2 \cos \left (\sqrt {3} x\right )+c_3 \sin \left (\sqrt {3} x\right )\right ) \]