Internal problem ID [848]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 6.4, The Laplace Transform. Differential equations with discontinuous forcing
functions. page 268
Problem number: 4.
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\le t <10 \\ 0 & \mathit {otherwise} \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: 0.188 (sec). Leaf size: 56
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=piecewise(0<=t and t<10,1,true,0),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (\left \{\begin {array}{cc} 0 & t <0 \\ 1-2 \,{\mathrm e}^{-t}+{\mathrm e}^{-2 t} & t <10 \\ 2 \,{\mathrm e}^{10-t}-{\mathrm e}^{20-2 t}-2 \,{\mathrm e}^{-t}+{\mathrm e}^{-2 t} & 10\le t \end {array}\right .\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 61
DSolve[{y''[t]+3*y'[t]+2*y[t]==Piecewise[{{1,0<=t<10},{0,True}}],{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 10 \\ \frac {1}{2} e^{-2 t} \left (-1+e^{10}\right ) \left (-1-e^{10}+2 e^t\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}