28.2.30 problem 30

Internal problem ID [4473]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 30
Date solved : Monday, January 27, 2025 at 09:19:12 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y&=5 \cos \left (2 x \right ) \end{align*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)+diff(y(x),x$2)+5*diff(y(x),x)+5*y(x)=5*cos(2*x),y(x), singsol=all)
 
\[ y \left (x \right ) = c_3 \sin \left (\sqrt {5}\, x \right )+{\mathrm e}^{-x} c_{1} +c_{2} \cos \left (\sqrt {5}\, x \right )+\cos \left (2 x \right )+2 \sin \left (2 x \right ) \]

Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 46

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]+5*D[y[x],x]+5*y[x]==5*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to 2 \sin (2 x)+\cos (2 x)+c_3 e^{-x}+c_1 \cos \left (\sqrt {5} x\right )+c_2 \sin \left (\sqrt {5} x\right ) \]