Internal problem ID [13642]
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: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x$6)+16*diff(y(x),x$3)+64*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{3 x} \left (c_{6} x +c_{4} \right ) \cos \left (\sqrt {3}\, x \right )+{\mathrm e}^{3 x} \left (c_{5} x +c_{3} \right ) \sin \left (\sqrt {3}\, x \right )+c_{2} x +c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ 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]
\[ y(x)\to e^{-2 x} \left (c_6 x+e^{3 x} (c_4 x+c_3) \cos \left (\sqrt {3} x\right )+e^{3 x} (c_2 x+c_1) \sin \left (\sqrt {3} x\right )+c_5\right ) \]