20.21.6 problem Problem 6

Internal problem ID [3933]
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 6
Date solved : Monday, January 27, 2025 at 08:04:43 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=5 \sin \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.696 (sec). Leaf size: 19

dsolve([diff(y(t),t)-y(t)=5*sin(2*t),y(0) = -1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 21

DSolve[{D[y[t],t]-y[t]==5*Sin[2*t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

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