84.38.15 problem 26.27

Internal problem ID [22369]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 26.27
Date solved : Thursday, October 02, 2025 at 08:38:00 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y&=5 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 23

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

\[ y = \frac {10 \,{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right )}{3}-5+\frac {5 \,{\mathrm e}^{t}}{3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

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

\begin{align*} y(t)&\to \frac {5}{3} \left (e^t+2 e^{-t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )-3\right ) \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = \frac {5 e^{t}}{3} - 5 + \frac {10 e^{- \frac {t}{2}} \cos {\left (\frac {\sqrt {3} t}{2} \right )}}{3} \]