Internal problem ID [4091]
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 20.29, 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 }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 32
DSolve[y''''[x]+4*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_4 x-\frac {1}{4} c_1 \cos (2 x)-\frac {1}{4} c_2 \sin (2 x)+c_3 \\ \end{align*}