Internal problem ID [5698]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.156 (sec). Leaf size: 71
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=piecewise(0<t and t<1,4*t,t>1,8),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left \{\begin {array}{cc} 2 t -{\mathrm e}^{-2 t}-3+4 \,{\mathrm e}^{-t} & t <1 \\ -{\mathrm e}^{-2}+1+4 \,{\mathrm e}^{-1} & t =1 \\ 3 \,{\mathrm e}^{-2 t +2}-8 \,{\mathrm e}^{1-t}-{\mathrm e}^{-2 t}+4+4 \,{\mathrm e}^{-t} & 1<t \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 70
DSolve[{y''[t]+3*y'[t]+2*y[t]==Piecewise[{{4*t,0<t<1},{8,t>1}}],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 0 \\ 2 t-e^{-2 t}+4 e^{-t}-3 & 0<t\leq 1 \\ e^{-2 t} \left (-1+3 e^2+4 e^t+4 e^{2 t}-8 e^{t+1}\right ) & \text {True} \\ \end {array} \\ \end {array} \]