28.2.34 problem 34

Internal problem ID [4477]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 34
Date solved : Monday, January 27, 2025 at 09:20:35 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=4*sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 29

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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