Internal problem ID [5703]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (1\right ) = 1+\cos \left (2\right ), y^{\prime }\left (1\right ) = 4-2 \sin \left (2\right )] \end {align*}
✓ Solution by Maple
Time used: 1.844 (sec). Leaf size: 87
dsolve([diff(y(t),t$2)+4*y(t)=piecewise(0<t and t<5,8*t^2,t>5,0),y(1) = 1+cos(2), D(y)(1) = 4-2*sin(2)],y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (2 t \right )+\left (\left \{\begin {array}{cc} 2 t^{2}-1 & t <5 \\ 10 \sin \left (2 t -10\right )+49 \cos \left (2 t -10\right ) & 5\le t \end {array}\right .\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 51
DSolve[{y''[t]+4*y[t]==Piecewise[{{8*t^2,0<t<5},{0,t>5}}],{y[1]==1+Cos[2],y'[1]==4-2*Sin[2]}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 2 t^2+\cos (2 t)-1 & 0<t\leq 5 \\ 49 \cos (2 (t-5))+\cos (2 t)-10 \sin (10-2 t) & t>5 \\ \end {array} \\ \end {array} \]