Internal problem ID [10943]
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 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }-12 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([4*diff(y(t),t$2)-12*diff(y(t),t)+13*y(t)=0,y(0) = 2, D(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = 2 \,{\mathrm e}^{\frac {3 t}{2}} \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[{4*y''[t]-12*y'[t]+13*y[t]==0,{y[0]==2,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{3 t/2} \cos (t) \\ \end{align*}