Internal problem ID [10985]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 4(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-\left (\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -6, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 50
dsolve([diff(y(t),t$2)-2*diff(y(t),t)=piecewise(0<=t and t<1,4,t>=1,6),y(0) = -6, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left \{\begin {array}{cc} -13+{\mathrm e}^{2 t} & t <0 \\ 3 \,{\mathrm e}^{2 t}-15-4 t & t <1 \\ 3 \,{\mathrm e}^{2 t}-14+{\mathrm e}^{2 t -2}-6 t & 1\le t \end {array}\right .\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 68
DSolve[{y''[t]-2*y'[t]==Piecewise[{{4,0<=t<1},{6,t>=1}}],{y[0]==-6,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} \frac {1}{2} \left (-13+e^{2 t}\right ) & t\leq 0 \\ \frac {1}{2} \left (-4 t+3 e^{2 t}-15\right ) & 0<t\leq 1 \\ -3 t+\frac {1}{2} e^{2 t-2} \left (1+3 e^2\right )-7 & \text {True} \\ \\ \\ \\ \\ \end{align*}