20.21.7 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 : Monday, January 27, 2025 at 08:04:44 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*}

✓ Solution by Maple

Time used: 3.546 (sec). Leaf size: 23

dsolve([diff(y(t),t)+y(t)=5*exp(t)*sin(t),y(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 27

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

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