28.2.1 problem 1

Internal problem ID [4444]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 1
Date solved : Monday, January 27, 2025 at 09:17:47 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

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

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