67.3.23 problem Problem 24

Internal problem ID [14041]
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 24
Date solved : Tuesday, January 28, 2025 at 06:13:08 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=-20 \end{align*}

✓ Solution by Maple

Time used: 8.854 (sec). Leaf size: 15

dsolve([diff(y(t),t$3)+4*diff(y(t),t$2)+29*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 5, (D@@2)(y)(0) = -20],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-2 t} \sin \left (5 t \right )+1 \]

✓ Solution by Mathematica

Time used: 0.273 (sec). Leaf size: 49

DSolve[{D[ y[t],{t,3}]+4*D[y[t],{t,2}]-20*D[y[t],t]==0,{y[0]==1,Derivative[1][y][0] ==5,Derivative[2][y][0] ==-20}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {5 e^{2 \left (\sqrt {6}-1\right ) t}}{4 \sqrt {6}}-\frac {5 e^{-2 \left (1+\sqrt {6}\right ) t}}{4 \sqrt {6}}+1 \]