Internal problem ID [13322]
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 (j).
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(diff(y(x),x$6)+16*diff(y(x),x$3)+64*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-2 x} x +c_{3} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+c_{4} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right )+c_{5} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right ) x +c_{6} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right ) x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 60
DSolve[y''''''[x]+16*y'''[x]+64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_6 x+e^{3 x} (c_4 x+c_3) \cos \left (\sqrt {3} x\right )+e^{3 x} (c_2 x+c_1) \sin \left (\sqrt {3} x\right )+c_5\right ) \]