23.3.8 problem 7(h)

Internal problem ID [4149]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(h)
Date solved : Monday, January 27, 2025 at 08:40:02 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)-diff(y(x),x$3)-9*diff(y(x),x$2)-11*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

DSolve[D[y[x],{x,4}]-D[y[x],{x,3}]-9*D[y[x],{x,2}]-11*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_3 x^2+c_2 x+c_4 e^{5 x}+c_1\right ) \]