Internal problem ID [10938]
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 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+5*y(t)=0,y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = 3 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[{y''[t]-4*y'[t]+5*y[t]==0,{y[0]==0,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 e^{2 t} \sin (t) \\ \end{align*}