Internal problem ID [2873]
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 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-3 y=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 3.907 (sec). Leaf size: 97
dsolve([diff(y(t),t)-3*y(t)=10*exp(-(t-a))*sin(2*(t-a))*Heaviside(t-a),y(0) = 5],y(t), singsol=all)
\[ y \left (t \right ) = \left (\operatorname {Heaviside}\left (t -a \right )+\operatorname {Heaviside}\left (a \right )-1\right ) {\mathrm e}^{-3 a +3 t}-\left (\left (\cos \left (2 t \right )+2 \sin \left (2 t \right )\right ) \cos \left (2 a \right )-2 \sin \left (2 a \right ) \left (\cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2}\right )\right ) {\mathrm e}^{-t +a} \operatorname {Heaviside}\left (t -a \right )-\left (\operatorname {Heaviside}\left (a \right )-1\right ) \left (\cos \left (2 a \right )-2 \sin \left (2 a \right )\right ) {\mathrm e}^{3 t +a}+5 \,{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.461 (sec). Leaf size: 103
DSolve[{y'[t]-3*y[t]==10*Exp[-(t-a)]*Sin[2*(t-a)]*UnitStep[t-a],{y[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 a-t} \left (e^{4 t} \theta (-a) \left (-2 e^{4 a} \sin (2 a)+e^{4 a} \cos (2 a)-1\right )+\theta (t-a) \left (2 e^{4 a} \sin (2 (a-t))-e^{4 a} \cos (2 (a-t))+e^{4 t}\right )+5 e^{3 a+4 t}\right ) \]