Internal problem ID [10950]
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 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {3 y^{\prime \prime }+8 y^{\prime }-3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([3*diff(y(t),t$2)+8*diff(y(t),t)-3*y(t)=0,y(0) = 3, D(y)(0) = -4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {3 \left ({\mathrm e}^{\frac {10 t}{3}}+1\right ) {\mathrm e}^{-3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[{3*y''[t]+8*y'[t]-3*y[t]==0,{y[0]==3,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3}{2} e^{-3 t} \left (e^{10 t/3}+1\right ) \\ \end{align*}