3.13 problem Problem 14

Internal problem ID [10947]

Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section: Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number: Problem 14.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 12

dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=0,y(0) = 0, D(y)(0) = -1],y(t), singsol=all)
 

\[ y \left (t \right ) = -\frac {{\mathrm e}^{t} \sin \left (2 t \right )}{2} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 14

DSolve[{y''[t]-2*y'[t]+5*+y[t]==0,{y[0]==0,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -e^t \sin (t) \cos (t) \\ \end{align*}