Internal problem ID [5921]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+13 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 14
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=0,y(0) = 0, D(y)(0) = -3],y(t), singsol=all)
\[ y \relax (t ) = -\frac {3 \,{\mathrm e}^{3 t} \sin \left (2 t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{y''[t]-6*y'[t]+13*y[t]==0,{y[0]==0,y'[0]==-3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -3 e^{3 t} \sin (t) \cos (t) \\ \end{align*}