Internal problem ID [2335]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-y+y^{\prime }-5 \sin \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(t),t)-y(t)=5*sin(2*t),y(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = -\sin \left (2 t \right )-2 \cos \left (2 t \right )+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 21
DSolve[{y'[t]-y[t]==5*Sin[2*t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t-\sin (2 t)-2 \cos (2 t) \\ \end{align*}