Internal problem ID [4947]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-\left (\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 8.516 (sec). Leaf size: 56
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=piecewise(0<t and t<1,1,t>1,0),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (\left \{\begin {array}{cc} 0 & t <0 \\ 1-2 \,{\mathrm e}^{-t}+{\mathrm e}^{-2 t} & t <1 \\ 2 \,{\mathrm e}^{-t +1}-{\mathrm e}^{-2 t +2}-2 \,{\mathrm e}^{-t}+{\mathrm e}^{-2 t} & 1\le t \end {array}\right .\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 57
DSolve[{y''[t]+3*y'[t]+2*y[t]==Piecewise[{{1,0<t<1},{0,t>1}}],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} 0 & t\leq 0 \\ \frac {1}{2} e^{-2 t} \left (-1+e^t\right )^2 & 0<t\leq 1 \\ \frac {1}{2} (-1+e) e^{-2 t} \left (-1-e+2 e^t\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}