Internal problem ID [5760]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section B,
Challenge Problems. Page 310
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {i^{\prime \prime }+2 i^{\prime }+3 i-\left (\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [i \relax (0) = 8, i^{\prime }\relax (0) = 0] \end {align*}
✗ Solution by Maple
dsolve([diff(i(t),t$2)+2*diff(i(t),t)+3*i(t)=piecewise(0<t and t<2*Pi,30,2*Pi<= t and t<= 5*Pi,0,5*Pi<t and t<infinity,10),i(0) = 8, D(i)(0) = 0],i(t), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.26 (sec). Leaf size: 289
DSolve[{i''[t]+2*i'[t]+3*i[t]==Piecewise[{{30,0<t<2*Pi},{0,2*Pi<= t <= 5*Pi},{10,5*Pi<t<Infinity}}],{i[0]==8,i'[0]==0}},i[t],t,IncludeSingularSolutions -> True]
\begin{align*} i(t)\to {cc} \{ & {cc} 10-e^{-t} \left (2 \cos \left (\sqrt {2} t\right )+\sqrt {2} \sin \left (\sqrt {2} t\right )\right ) & 0<t\leq 2 \pi \\ 4 e^{-t} \left (2 \cos \left (\sqrt {2} t\right )+\sqrt {2} \sin \left (\sqrt {2} t\right )\right ) & t\leq 0 \\ e^{-t} \left (-2 \cos \left (\sqrt {2} t\right )-\sqrt {2} \sin \left (\sqrt {2} t\right )+5 e^{2 \pi } \left (2 \cos \left (\sqrt {2} (t-2 \pi )\right )+\sqrt {2} \sin \left (\sqrt {2} (t-2 \pi )\right )\right )\right ) & 2 \pi <t\leq 5 \pi \\ \frac {1}{3} e^{-t} \left (-6 \cos \left (\sqrt {2} t\right )+10 e^t-3 \sqrt {2} \sin \left (\sqrt {2} t\right )-5 e^{5 \pi } \left (2 \cos \left (\sqrt {2} (t-5 \pi )\right )+\sqrt {2} \sin \left (\sqrt {2} (t-5 \pi )\right )\right )+15 e^{2 \pi } \left (2 \cos \left (\sqrt {2} (t-2 \pi )\right )+\sqrt {2} \sin \left (\sqrt {2} (t-2 \pi )\right )\right )\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}