Internal problem ID [5922]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+20 y^{\prime }+51 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.034 (sec). Leaf size: 34
dsolve([2*diff(y(t),t$2)+20*diff(y(t),t)+51*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = 10 \sqrt {2}\, {\mathrm e}^{-5 t} \sin \left (\frac {t \sqrt {2}}{2}\right )+2 \,{\mathrm e}^{-5 t} \cos \left (\frac {t \sqrt {2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{2*y''[t]+20*y'[t]+51*y[t]==0,{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{-5 t} \left (5 \sqrt {2} \sin \left (\frac {t}{\sqrt {2}}\right )+\cos \left (\frac {t}{\sqrt {2}}\right )\right ) \\ \end{align*}