84.38.9 problem 26.21

Internal problem ID [22363]
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 : 26.21
Date solved : Thursday, October 02, 2025 at 08:37:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 27

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

\[ y = -\frac {{\mathrm e}^{-3 t}}{26}+\frac {{\mathrm e}^{t}}{10}-\frac {4 \cos \left (2 t \right )}{65}-\frac {7 \sin \left (2 t \right )}{65} \]

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 34

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

\begin{align*} y(t)&\to \frac {1}{130} \left (-5 e^{-3 t}+13 e^t-14 \sin (2 t)-8 \cos (2 t)\right ) \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \frac {e^{t}}{15} - \frac {\sin {\left (2 t \right )}}{15} - \frac {e^{- t}}{15} \]