44.1.56 problem 71

Internal problem ID [6931]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 71
Date solved : Monday, January 27, 2025 at 02:37:14 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve(diff(y(x),x$4)-20*diff(y(x),x$3)+158*diff(y(x),x$2)-580*diff(y(x),x)+841*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x} \left (\left (c_4 x +c_{2} \right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_3 x +c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[x],{x,4}]-20*D[y[x],{x,3}]+158*D[y[x],{x,2}]-580*D[y[x],x]+841*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{5 x} ((c_4 x+c_3) \cos (2 x)+(c_2 x+c_1) \sin (2 x)) \]