Internal problem ID [10960]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number: Problem 27.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = 5, y^{\prime \prime \prime }\left (0\right ) = 19] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(t),t$4)+13*diff(y(t),t$2)+36*y(t)=0,y(0) = 0, D(y)(0) = -1, (D@@2)(y)(0) = 5, (D@@3)(y)(0) = 19],y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (2 t \right )+\sin \left (2 t \right )-\cos \left (3 t \right )-\sin \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[{y''''[t]+13*y''[t]+36*y[t]==0,{y[0]==0,y'[0]==-1,y''[0]==5,y'''[0]==19}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sin (2 t)-\sin (3 t)+\cos (2 t)-\cos (3 t) \\ \end{align*}