Internal problem ID [5233]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 83
Problem number: 1(e).
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 }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-5*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{x}+c_{4} {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[y''''[x]-5*y''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (c_4 e^x+c_3\right )+c_1\right ) \\ \end{align*}