Internal problem ID [5108]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y-3 \sin \left (t \right )+5 \cos \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \left (-\frac {5}{4}-\frac {3}{4} t +\frac {5}{8} t^{2}\right ) \cos \left (t \right )+\left (\frac {3}{4}-\frac {5}{4} t -\frac {3}{8} t^{2}\right ) \sin \left (t \right )+\cos \left (t \right ) c_{1} +c_{2} \sin \left (t \right )+c_{3} t \cos \left (t \right )+c_{4} t \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.119 (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*}