28.2.22 problem 22

Internal problem ID [4465]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 22
Date solved : Monday, January 27, 2025 at 09:19:06 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right ) \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+4*y(x)=sin(x)*cos(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (40 c_3 +\sin \left (x \right )\right ) \cos \left (x \right )^{2}}{20}+\frac {\left (24 c_4 \sin \left (x \right )+x +12 c_{1} \right ) \cos \left (x \right )}{12}+\frac {\left (360 c_{2} -7\right ) \sin \left (x \right )}{360}-c_3 \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 50

DSolve[D[y[x],{x,4}]+5*D[y[x],{x,2}]+4*y[x]==Sin[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)}{72}+\frac {1}{80} \sin (3 x)+\left (\frac {x}{12}+c_3\right ) \cos (x)+c_1 \cos (2 x)+c_4 \sin (x)+c_2 \sin (2 x) \]