Internal problem ID [2870]
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`]]
\[ \boxed {y^{\prime }+2 y=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 2.312 (sec). Leaf size: 43
dsolve([diff(y(t),t)+2*y(t)=Heaviside(t-Pi)*sin(2*t),y(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -\pi \right ) {\mathrm e}^{-2 t +2 \pi }}{4}+\frac {\operatorname {Heaviside}\left (t -\pi \right ) \left (-\cos \left (2 t \right )+\sin \left (2 t \right )\right )}{4}+3 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 55
DSolve[{y'[t]+2*y[t]==UnitStep[t-Pi]*Sin[2*t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 3 e^{-2 t} & t\leq \pi \\ \frac {1}{4} e^{-2 t} \left (-e^{2 t} \cos (2 t)+e^{2 t} \sin (2 t)+e^{2 \pi }+12\right ) & \text {True} \\ \end {array} \\ \end {array} \]