Internal problem ID [5701]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT
KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 34
dsolve([diff(y(t),t$2)+y(t)=piecewise(0<t and t<1,t,t>1,0),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left \{\begin {array}{cc} 0 & t <0 \\ -\sin \left (t \right )+t & t <1 \\ -\sin \left (t \right )+\cos \left (t -1\right )+\sin \left (t -1\right ) & 1\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 44
DSolve[{y''[t]+y[t]==Piecewise[{{t,0<t<1},{0,t>1}}],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} t-\sin (t) & 0<t\leq 1 \\ \cos (1-t)-\sin (1-t)-\sin (t) & t>1 \\ \end {array} \\ \end {array} \]