Internal problem ID [14911]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.3, page 249
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=\left \{\begin {array}{cc} t & 0\le t <1 \\ -t +2 & 1\le t <2 \\ 0 & 2\le t \end {array}\right .} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 56
dsolve([diff(x(t),t$2)+x(t)=piecewise(0<=t and t<1,t,t>=1 and t<2,2-t,t>=2,0),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \left \{\begin {array}{cc} 0 & t <0 \\ t -\sin \left (t \right ) & t <1 \\ 2 \sin \left (t -1\right )-\sin \left (t \right )-t +2 & t <2 \\ 2 \sin \left (t -1\right )-\sin \left (t \right )-\sin \left (t -2\right ) & 2\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 63
DSolve[{x''[t]+x[t]==Piecewise[{{t,0<=t<1},{2-t,1<=t<2},{0,t>=2}}],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 0 \\ t-\sin (t) & 0<t\leq 1 \\ -t-2 \sin (1-t)-\sin (t)+2 & 1<t\leq 2 \\ -4 \sin ^2\left (\frac {1}{2}\right ) \sin (1-t) & \text {True} \\ \end {array} \\ \end {array} \]