Internal problem ID [2360]
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 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-y-4 \theta \left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 39
dsolve([diff(y(t),t)-y(t)=4*Heaviside(t-Pi/4)*cos(t-Pi/4),y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \left (-2 \cos \left (t +\frac {\pi }{4}\right )+2 \,{\mathrm e}^{t -\frac {\pi }{4}}-2 \sin \left (t +\frac {\pi }{4}\right )\right ) \theta \left (t -\frac {\pi }{4}\right )+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 40
DSolve[{y'[t]-y[t]==4*UnitStep[t-Pi/4]*Cos[t-Pi/4],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} e^t & 4 t\leq \pi \\ -2 \sqrt {2} \cos (t)+e^t+2 e^{t-\frac {\pi }{4}} & \text {True} \\ \\ \\ \\ \\ \end{align*}