Internal problem ID [4089]
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 20.27, 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 }+4 y^{\prime \prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (x \sqrt {2}\right )+c_{2} \cos \left (x \sqrt {2}\right )+c_{3} \sin \left (x \sqrt {2}\right ) x +c_{4} \cos \left (x \sqrt {2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 38
DSolve[y''''[x]+4*y''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \cos \left (\sqrt {2} x\right )+(c_4 x+c_3) \sin \left (\sqrt {2} x\right ) \\ \end{align*}