20.12.2 problem Problem 8

Internal problem ID [3796]
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 8.10, Chapter review. page 575
Problem number : Problem 8
Date solved : Monday, January 27, 2025 at 08:02:25 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$3)+11*diff(y(x),x$2)+36*diff(y(x),x)+26*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]+11*D[y[x],{x,2}]+36*D[y[x],x]+26*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (c_3 e^{4 x}+c_2 \cos (x)+c_1 \sin (x)\right ) \]