Internal problem ID [13890]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 30. Piecewise-defined functions and periodic functions. Additional Exercises.
page 553
Problem number: 30.10 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.844 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)=piecewise(t<1,0,1<t and t<3,1,t>3,0),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left \{\begin {array}{cc} 0 & t <1 \\ \frac {\left (t -1\right )^{2}}{2} & t <3 \\ 2 t -4 & 3\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 33
DSolve[{y''[t]==Piecewise[{ {0,t<1},{1,1<t<3},{0,t>3}}],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 1 \\ \frac {1}{2} (t-1)^2 & 1<t\leq 3 \\ 2 (t-2) & \text {True} \\ \end {array} \\ \end {array} \]