20.6.11 problem Problem 33

Internal problem ID [3706]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 33
Date solved : Monday, January 27, 2025 at 07:55:40 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-13*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_4 \,{\mathrm e}^{6 x}+c_3 \,{\mathrm e}^{5 x}+c_{2} {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]-13*D[y[x],{x,2}]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^x+e^{5 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]