Internal problem ID [5928]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\left (\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.531 (sec). Leaf size: 39
dsolve([diff(y(t),t)+y(t)=piecewise(0<=t and t<1,1,t>=1,-1),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \left \{\begin {array}{cc} 0 & t <0 \\ 1-{\mathrm e}^{-t} & t <1 \\ -1+2 \,{\mathrm e}^{-t +1}-{\mathrm e}^{-t} & 1\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 40
DSolve[{y'[t]+y[t]==Piecewise[{{1,0<=t<1},{-1,t>=1}}],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} 0 & t\leq 0 \\ -\cosh (t)+\sinh (t)+1 & 0<t\leq 1 \\ -1+e^{-t} (-1+2 e) & \text {True} \\ \\ \\ \\ \\ \end{align*}