87.22.10 problem 10

Internal problem ID [23755]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 4. The Laplace transform. Exercise at page 199
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:44:55 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-27 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ y^{\prime }\left (0\right )&=6 \\ y^{\prime \prime }\left (0\right )&=18 \\ \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 22

ode:=diff(diff(diff(y(t),t),t),t)-27*y(t) = 0; 
ic:=[y(0) = -1, D(y)(0) = 6, (D@@2)(y)(0) = 18]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 31

ode=D[y[t],{t,3}]-27*y[t]==0; 
ic={y[0]==-1,Derivative[1][y][0] ==6,Derivative[2][y][0] ==18}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.141 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-27*y(t) + Derivative(y(t), (t, 3)),0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): 6, Subs(Derivative(y(t), (t, 2)), t, 0): 18} 
dsolve(ode,func=y(t),ics=ics)
 

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