Internal problem ID [13318]
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 (f).
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}-2 y^{\prime \prime \prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 68
dsolve(diff(y(x),x$6)-2*diff(y(x),x$3)+y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x +c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{4} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{5} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) x +c_{6} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 67
DSolve[y''''''[x]-2*y'''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (e^{3 x/2} (c_6 x+c_5)+(c_4 x+c_3) \cos \left (\frac {\sqrt {3} x}{2}\right )+(c_2 x+c_1) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]