67.3.26 problem Problem 27

Internal problem ID [14044]
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
Date solved : Tuesday, January 28, 2025 at 06:13:10 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \end{align*}

Using Laplace method 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: 9.614 (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)
 

\[ y = \cos \left (2 t \right )+\sin \left (2 t \right )-\cos \left (3 t \right )-\sin \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 26

DSolve[{D[y[t],{t,4}]+13*D[y[t],{t,2}]+36*y[t]==0,{y[0]==0,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==5,Derivative[3][y][0]==19}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sin (2 t)-\sin (3 t)+\cos (2 t)-\cos (3 t) \]