87.22.14 problem 14

Internal problem ID [23759]
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 : 14
Date solved : Thursday, October 02, 2025 at 09:44:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=6 \\ y^{\prime }\left (0\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)+2*y(t) = 24*cosh(t); 
ic:=[y(0) = 6, D(y)(0) = -3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{-t}+7 \,{\mathrm e}^{2 t}+\left (-12 t -3\right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 30

ode=D[y[t],{t,2}]-3*D[y[t],{t,1}]+2*y[t]==24*Cosh[t]; 
ic={y[0]==6,Derivative[1][y][0] ==-3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -3 e^t (4 t+1)+2 e^{-t}+7 e^{2 t} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) - 24*cosh(t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 6, Subs(Derivative(y(t), t), t, 0): -3} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -2*y(t)/3 + 8*cosh(t) + Derivative(y(t), t) - Derivative(y(t), (