Internal problem ID [3263]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 22.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y=\sin \left (x \right ) \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (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: 0.04 (sec). Leaf size: 50
DSolve[y''''[x]+5*y''[x]+4*y[x]==Sin[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (x)}{72}+\frac {1}{80} \sin (3 x)+\left (\frac {x}{12}+c_3\right ) \cos (x)+c_1 \cos (2 x)+c_4 \sin (x)+c_2 \sin (2 x) \]