61.3.23 problem Problem 24

Internal problem ID [15322]
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 : Thursday, October 02, 2025 at 10:11:37 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*}

✓ Maple. Time used: 0.102 (sec). Leaf size: 15

ode:=diff(diff(diff(y(t),t),t),t)+4*diff(diff(y(t),t),t)+29*diff(y(t),t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 5, (D@@2)(y)(0) = -20]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 49

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

\begin{align*} 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 \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(29*Derivative(y(t), t) + 4*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 5, Subs(Derivative(y(t), (t, 2)), t, 0): -20} 
dsolve(ode,func=y(t),ics=ics)
 

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