87.22.27 problem 27

Internal problem ID [23772]
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 : 27
Date solved : Thursday, October 02, 2025 at 09:45:02 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y&=12 \sinh \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=6 \\ y^{\prime }\left (0\right )&=-1 \\ y^{\prime \prime }\left (0\right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.171 (sec). Leaf size: 32

ode:=diff(diff(diff(y(t),t),t),t)-y(t) = 12*sinh(t); 
ic:=[y(0) = 6, D(y)(0) = -1, (D@@2)(y)(0) = 7]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = {\mathrm e}^{t} \left (2 t +1\right )+3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) \]

✓ Mathematica. Time used: 0.179 (sec). Leaf size: 42

ode=D[y[t],{t,3}]-y[t]==12*Sinh[t]; 
ic={y[0]==6,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==7}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t (2 t+1)+3 e^{-t}+2 e^{-t/2} \cos \left (\frac {\sqrt {3} t}{2}\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 12*sinh(t) + Derivative(y(t), (t, 3)),0) 
ics = {y(0): 6, Subs(Derivative(y(t), t), t, 0): -1, Subs(Derivative(y(t), (t, 2)), t, 0): 7} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Could not solve `-y(t) - 12*sinh(t) + Derivative(y(t), (t, 3))` using the meth