Internal problem ID [13886]
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: 30.6 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=\operatorname {Heaviside}\left (-2+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.656 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)=Heaviside(t-2),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -2\right ) \left (t -2\right )^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 21
DSolve[{y''[t]==UnitStep[t-2],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{2} (t-2)^2 & t>2 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]