Internal problem ID [4087]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.25, page 220.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 37
dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sqrt {3}\, x \right )+c_{2} \cos \left (\sqrt {3}\, x \right )+c_{3} \sin \left (x \sqrt {2}\right )+c_{4} \cos \left (x \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 50
DSolve[y''''[x]+5*y''[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 \cos \left (\sqrt {2} x\right )+c_1 \cos \left (\sqrt {3} x\right )+c_4 \sin \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \\ \end{align*}