Internal problem ID [12449]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 10.
ODE order: 8.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(diff(y(x),x$8)+8*diff(y(x),x$4)+16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \sin \left (x \right )+c_{2} {\mathrm e}^{-x} \cos \left (x \right )+c_{3} {\mathrm e}^{-x} \sin \left (x \right ) x +c_{4} {\mathrm e}^{-x} \cos \left (x \right ) x +c_{5} {\mathrm e}^{x} \sin \left (x \right )+c_{6} {\mathrm e}^{x} \cos \left (x \right )+c_{7} {\mathrm e}^{x} \sin \left (x \right ) x +c_{8} {\mathrm e}^{x} \cos \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 66
DSolve[D[y[x],{x,8}]+8*y''''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (c_4 x+c_7 e^{2 x}+c_8 e^{2 x} x+c_3\right ) \cos (x)+\left (c_2 x+c_5 e^{2 x}+c_6 e^{2 x} x+c_1\right ) \sin (x)\right ) \]