Internal problem ID [1719]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }+6 y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(3*diff(y(t),t$2)+6*diff(y(t),t)+3*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{-t} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[3*y''[t]+6*y'[t]+3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} (c_2 t+c_1) \\ \end{align*}