Internal problem ID [1724]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = v] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 1, D(y)(0) = v],y(t), singsol=all)
\[ y \relax (t ) = \left (3+v \right ) {\mathrm e}^{-2 t}+\left (-v -2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[{y''[t]+5*y'[t]+6*y[t]==0,{y[0]==1,y'[0]==v}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t} \left (e^t (v+3)-v-2\right ) \\ \end{align*}