14.21.7 problem Problem 7

Internal problem ID [3934]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 7
Date solved : Tuesday, September 30, 2025 at 06:59:13 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.133 (sec). Leaf size: 23

ode:=diff(y(t),t)+y(t) = 5*exp(t)*sin(t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 27

ode=D[y[t],t]+y[t]==5*Exp[t]*Sin[t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.095 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 5*exp(t)*sin(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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