28.2.29 problem 29

Internal problem ID [4472]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 29
Date solved : Monday, January 27, 2025 at 09:19:11 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 58

dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)-y(x)=44*sin(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \sin \left (3 x \right )+c_4 \,{\mathrm e}^{-\sqrt {\sqrt {5}-2}\, x}+c_{2} {\mathrm e}^{\sqrt {\sqrt {5}-2}\, x}+c_3 \sin \left (\sqrt {\sqrt {5}+2}\, x \right )+c_{1} \cos \left (\sqrt {\sqrt {5}+2}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 81

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,2}]-y[x]==44*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (3 x)+c_3 e^{\sqrt {\sqrt {5}-2} x}+c_4 e^{-\sqrt {\sqrt {5}-2} x}+c_1 \cos \left (\sqrt {2+\sqrt {5}} x\right )+c_2 \sin \left (\sqrt {2+\sqrt {5}} x\right ) \]