Internal problem ID [6681]
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`]]
\[ \boxed {y^{\prime }+y=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.14 (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)
\[ y \left (t \right ) = \left \{\begin {array}{cc} 0 & t <0 \\ 1-{\mathrm e}^{-t} & t <1 \\ 2 \,{\mathrm e}^{-t +1}-1-{\mathrm e}^{-t} & 1\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 43
DSolve[{y'[t]+y[t]==Piecewise[{{1,0<=t<1},{-1,t>=1}}],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 0 \\ 1-e^{-t} & 0<t\leq 1 \\ -e^{-t} \left (1-2 e+e^t\right ) & \text {True} \\ \end {array} \\ \end {array} \]