Internal problem ID [10940]
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 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+37 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+37*y(t)=0,y(0) = 2, D(y)(0) = -3],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {2 \,{\mathrm e}^{\frac {t}{2}} \left (2 \sin \left (3 t \right )-3 \cos \left (3 t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[{4*y''[t]-4*y'[t]+37*y[t]==0,{y[0]==2,y'[0]==-3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2}{3} e^{t/2} (3 \cos (3 t)-2 \sin (3 t)) \\ \end{align*}