Internal problem ID [2754]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y-\sin \relax (x ) \cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 40
dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+4*y(x)=sin(x)*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \cos \relax (x )}{12}+\frac {\sin \left (3 x \right )}{80}-\frac {\sin \relax (x )}{144}+\cos \relax (x ) c_{1}+c_{2} \sin \relax (x )+c_{3} \cos \left (2 x \right )+c_{4} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 48
DSolve[y''''[x]+5*y''[x]+4*y[x]==Sin[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{80} \sin (3 x)+\left (\frac {x}{12}+c_3\right ) \cos (x)+c_1 \cos (2 x)+\left (\frac {1}{72}+c_4\right ) \sin (x)+c_2 \sin (2 x) \\ \end{align*}