Internal problem ID [5109]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.35.
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 }+2 y^{\prime \prime }+y-3 \sin \relax (t )+5 \cos \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(diff(y(t),t$4)+2*diff(y(t),t$2)+y(t)=3*sin(t)-5*cos(t),y(t), singsol=all)
\[ y \relax (t ) = \left (-\frac {5}{4}-\frac {3}{4} t +\frac {5}{8} t^{2}\right ) \cos \relax (t )+\left (-\frac {5}{4} t +\frac {3}{4}-\frac {3}{8} t^{2}\right ) \sin \relax (t )+\cos \relax (t ) c_{1}+c_{2} \sin \relax (t )+c_{3} \cos \relax (t ) t +c_{4} \sin \relax (t ) t \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 51
DSolve[y''''[t]+2*y''[t]+y[t]==3*Sin[t]-5*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{16} ((2 t (5 t-3+8 c_2)-25+16 c_1) \cos (t)+(-6 t (t+5)+16 c_4 t+3+16 c_3) \sin (t)) \\ \end{align*}