28.2.48 problem 48

Internal problem ID [4491]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 48
Date solved : Monday, January 27, 2025 at 09:21:38 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=2*exp(x)+5*exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==2*Exp[x]+5*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x+e^x-1+c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]