Internal problem ID [829]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 15.
ODE order: 8.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (8)}+8 y^{\prime \prime \prime \prime }+16 y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} \sin \relax (x ) {\mathrm e}^{x}+c_{2} \cos \relax (x ) {\mathrm e}^{x}+c_{3} \sin \relax (x ) {\mathrm e}^{x} x +c_{4} \cos \relax (x ) {\mathrm e}^{x} x +c_{5} \sin \relax (x ) {\mathrm e}^{-x}+c_{6} \cos \relax (x ) {\mathrm e}^{-x}+c_{7} \sin \relax (x ) {\mathrm e}^{-x} x +c_{8} \cos \relax (x ) {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 238
DSolve[D[y[x],{x,8}]+8*y''''[x]+3*y'''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,2\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,5\right ]\right )+c_6 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,6\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,4\right ]\right )+c_7 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,7\right ]\right )+c_8 \exp \left (x \text {Root}\left [\text {$\#$1}^8+8 \text {$\#$1}^4+3 \text {$\#$1}^3+16\&,8\right ]\right ) \\ \end{align*}