87.22.4 problem 4

Internal problem ID [23749]
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 : 4
Date solved : Thursday, October 02, 2025 at 09:44:52 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 23

ode:=diff(y(t),t)-3*y(t) = 13*cos(2*t); 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 24

ode=D[y[t],{t,1}]-3*y[t]==13*Cos[2*t]; 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.106 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) - 13*cos(2*t) + Derivative(y(t), t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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