Internal problem ID [2361]
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 10.7.
page 704
Problem number: Problem 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+2 y-\theta \left (-\pi +t \right ) \sin \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 46
dsolve([diff(y(t),t)+2*y(t)=Heaviside(t-Pi)*sin(2*t),y(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = \frac {\theta \left (-\pi +t \right ) {\mathrm e}^{-2 t +2 \pi }}{4}+\frac {\left (-\cos \left (2 t \right )+\sin \left (2 t \right )\right ) \theta \left (-\pi +t \right )}{4}+3 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 46
DSolve[{y'[t]+2*y[t]==UnitStep[t-Pi]*Sin[2*t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} 3 e^{-2 t} & t\leq \pi \\ \frac {1}{4} \left (-\cos (2 t)+\sin (2 t)+e^{-2 t} \left (12+e^{2 \pi }\right )\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}