Internal problem ID [12333]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = -6, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 7.703 (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)
\[ y \left (t \right ) = -\frac {\left (\left \{\begin {array}{cc} 15+4 t -3 \,{\mathrm e}^{2 t} & t <1 \\ 20-3 \,{\mathrm e}^{2} & t =1 \\ 14+6 t -3 \,{\mathrm e}^{2 t}-{\mathrm e}^{2 t -2} & 1<t \end {array}\right .\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.056 (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]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{2} \left (-13+e^{2 t}\right ) & t\leq 0 \\ \frac {1}{2} \left (-4 t+3 e^{2 t}-15\right ) & 0<t\leq 1 \\ \frac {1}{2} \left (-6 t+3 e^{2 t}+e^{2 t-2}-14\right ) & \text {True} \\ \end {array} \\ \end {array} \]