Internal problem ID [4950]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\left (\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = \cos \relax (2)+1, y^{\prime }\relax (1) = 4-2 \sin \relax (2)] \end {align*}
✓ Solution by Maple
Time used: 0.353 (sec). Leaf size: 47
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)
\[ y \relax (t ) = \left \{\begin {array}{cc} 0 & t <0 \\ 2 t^{2}+\cos \left (2 t \right )-1 & t <5 \\ 10 \sin \left (-10+2 t \right )+49 \cos \left (-10+2 t \right )+\cos \left (2 t \right ) & 5\le t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.011 (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]
\begin{align*} y(t)\to {cc} \{ & {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{align*}