Internal problem ID [292]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 17.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(6*diff(y(x),x$4)+11*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\frac {2 \sqrt {3}\, x}{3}\right )+c_{2} \cos \left (\frac {2 \sqrt {3}\, x}{3}\right )+c_{3} \sin \left (\frac {\sqrt {2}\, x}{2}\right )+c_{4} \cos \left (\frac {\sqrt {2}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 94
DSolve[y''''[x]+11*y''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 \cos \left (\sqrt {\frac {1}{2} \left (11-\sqrt {105}\right )} x\right )+c_1 \cos \left (\sqrt {\frac {1}{2} \left (11+\sqrt {105}\right )} x\right )+c_4 \sin \left (\sqrt {\frac {1}{2} \left (11-\sqrt {105}\right )} x\right )+c_2 \sin \left (\sqrt {\frac {1}{2} \left (11+\sqrt {105}\right )} x\right ) \\ \end{align*}