28.2.46 problem 46

Internal problem ID [4489]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 46
Date solved : Monday, January 27, 2025 at 09:21:37 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=15 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=15*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 32

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==15*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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