Internal problem ID [2364]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-3 y+10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \theta \left (t -a \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 96
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)
\[ y \relax (t ) = 2 \left (\theta \left (t -a \right ) \left (\sin \left (-2 t +2 a \right )-\frac {\cos \left (-2 t +2 a \right )}{2}\right ) {\mathrm e}^{4 a -4 t}-\frac {\left (\theta \relax (a )-1\right ) \left (\cos \left (2 a \right )-2 \sin \left (2 a \right )\right ) {\mathrm e}^{4 a}}{2}+\frac {\theta \left (t -a \right )}{2}+\frac {5 \,{\mathrm e}^{3 a}}{2}+\frac {\theta \relax (a )}{2}-\frac {1}{2}\right ) {\mathrm e}^{3 t -3 a} \]
✓ Solution by Mathematica
Time used: 0.458 (sec). Leaf size: 88
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]
\begin{align*} y(t)\to e^{3 t-3 a} \left (\theta (t-a)+\theta (-a) \left (e^{4 a} (\cos (2 a)-2 \sin (2 a))-1\right )+5 e^{3 a}\right )-e^{a-t} \theta (t-a) (\cos (2 (a-t))-2 \sin (2 (a-t))) \\ \end{align*}