Internal problem ID [5907]
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. 7.2.2 TRANSFORMS OF DERIVATIVES
Page 289
Problem number: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {4 \,{\mathrm e}^{-t}}{3}-\frac {{\mathrm e}^{-4 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[{y''[t]+5*y'[t]+4*y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-4 t} \left (4 e^{3 t}-1\right ) \\ \end{align*}