49.9.5 problem 1(e)

Internal problem ID [7654]
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)
Date solved : Monday, January 27, 2025 at 03:09:05 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-5*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{4 x}+c_4 \,{\mathrm e}^{3 x}+{\mathrm e}^{x} c_{1} +c_3 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]-5*D[y[x],{x,2}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]