Internal problem ID [830]
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: 16.
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 }+2 y^{\prime \prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \relax (x )+c_{2} \cos \relax (x )+c_{3} \sin \relax (x ) x +c_{4} \cos \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y''''[x]+2*y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \cos (x)+(c_4 x+c_3) \sin (x) \\ \end{align*}